There are various ways to get a car airborne for one second, get involved in a major crash that sends you flying through the air or hit a Demolition Derby track ramp at the right speed and angle.
The easiest way to do this is in a Pro Touge race. Go to Race Day (single race), select Pro Touge as the discipline, Mount Haruna as the location and Peak Run as the route. After exiting the first overpass, there will soon be a wooden fence to the left that runs along the track for a few corners. Drive through it to get some nice airtime. It is very likely that you will have to try it a few times to find the right spot, because the games registers a 'fatal crash' relatively fast after you go through the barrier. Also, always go for the Instant Replay and rewind after you have crashed, this can help unlock the achievement.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

Transmission type can be changed under 'Driver Assists' in the pre race menu. Shifting up is done with the button and shifting down is done with the button.
There are two easy ways to achieve this. The first is to start a Race Day event, select a short narrow track (for example San Francisco Short Circuit) and select a fast, but controllable car. Set the difficulty to 'Basic', 'Grid position' to 'Front' and the number of laps to one. This way you are ensured of a first place start. The narrow track will help you to block off opponents. Don't try this when you are new to GRID and the racing genre, get familiar with the game and the racing style and you will soon know when to change gears.
If you are familiar with racing games and want to get the achievement fast, start your career and do the first 'Driver offer' race in Europe, after this first race you will unlock a time trial for BMW on the Nurburgring. It's a three lap challenge and you have to set a time of 1:47:00 for the bonus. This is not necessary for the achievement, the only thing you have to do is finish. Mind you that this can only be done in the very beginning of the career mode, later on you will have some opporunities to do another time trial in the Driver Offers, but these pop up quite random.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

To lap an opponent he has to be driving one lap behind you and then you overtake him. For example your opponent is in lap 3 and you are in lap 4 and you are closing on his tail. After you passed him he will be one full lap behind you and you have lapped him.
This is easiest achieved in a Demolition Derby (in GRID World available in the ARL region). Opponents in this discipline will frequently roll onto their roofs or crash into walls immobilizing themselves in that way. The game will still count them as being on track and participating in the race. Lap on of these opponents to unlock the achievement. This can only be done with at least 12 cars on track.
Can be done in GRID World (career) and Race Day (single race).

You have to finish the race with the rest of the field at least one lap behind. This is easiest done when attempting the 'Last Man Standing' achievement. After you have taken out all the competitors, finish the race and the achievement will unlock. Note that it will not unlock during the race, only after you finished.
Can be done in GRID World (career) or Race Day (single race).

This achievement will be unlocked during the course of the career. If you want to get it faster, start a Race Day event and choose one of the disciplines that feature 12 cars. These disciplines are: Prototype, GT1, GT2, Demolition Derby, Pro Tuned and Open Wheel. There are other disciplines in which you have 12 cars on the track at certain circuits, but that is not at all circuits.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

In total there are seven cities in the game, complete a race in all of them. The seven cities are:
San Francisco – North America – ARL League
Washington – North America – ARL League
Detroit – North America – ARL League
Long Beach – North America – ARL League
Milan – Europe – Euro League
Yokohama – Japan – J-Speed League
Shibuya – Japan – J-Speed League
In the career all these cities, but Shibuya, are available in the first license category. Shibuya is available in the second J-Speed license events.
The race locations are accumulated over GRID World (career), Race Day, (single race) and multiplayer.

You have to be involved in a crash with at least three other cars. The easiest to achieve this is not to brake for the first corner and plow your car into the pack of cars going into the turn. Whether you deliberately go after this achievement or not, it is one you will unlock with relative ease.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

After accumulating 1.000.000 reputation points in GRID World (career), you will unlock the six events of the Global License. Enter an event that your team mate is specialised in and finish 1st and 2nd in the overall classification. Finishing in 1st and 2nd in just one race is not enough, you have to be in the top two positions at the end of the event. Also, winning the Le Mans 24 Hours race with your team mate being 2nd, does not count, even though these races are designated as global events.
Can only be done in GRID World (career).

Every time you score a 'Great Drift' in a drift race you get another multiplier. This means you have to score 49 'Great Drifts' to get the achievement. Make sure you do not lose your combo, by making small drifts on the straights of the circuit you are driving on. These may not add to your multiplier, but they ensure you keep your combo.
To get a x50 multiplayer in a Drift event (Freestyle, Drift GP or ? discipline) you will need to be able to balance the gas and the steering in just the right way. If you spin out, you will lose your combo and the same thing will most likely happen if you quit a drift before the end of the corner, because you were not driving fast enough.
The tracks and cars on/with which to accomplish this are really dependent on your personal preferences. Two good tracks are the Okutama Drift Circuit, which is wide and does not have long straights, or the Yokohama Freestyle tracks. These let you decide your own route.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

To drift your car for five seconds you will need a delicate balance between angle and speed. If you go to slow or if the angle is too low, the drift will stop, if you go to fast or the angle is too high, chances are that you will spin out or finish the corner very fast. Play with the throttle and steering to get the ideal speed and angle, it might require a bit of practice.
Two good tracks to get this achievement on are the Okutama Drift Circuit, which has a lot of long and winding corners, and the Long Beach Classic Circuit, which features one long 360 degrees corner. On both tracks it is possible to get a drift of around six seconds.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

This achievement is accumulative, every time you roll you car it is added to the total. After you have made 20 rolls, the achievement will unlock. If you roll your car and restart the race, the roll will still count. So don't hesitate to restart to save your race position. Using a Flashback will cause the roll not to count.
On the Washington circuits there are a lot of tire stacks that stick out onto the circuit, if you hit one of these it will likely send you flying (and rolling) through the air. If you do a one lap race on the short circuit, you can easily score about four rolls in one race.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

You have to drive over 200mph during a race. The description says it has to be done during a GRID World (career) race, but it can also be done during a Race Day (single race) and multiplayer race.
The easiest way to do this is in a Race Day race. Select the ’24 Hours of Le Mans’ as discipline and choose one of the LMP1 cars (Audi R10 TDI, Courage LC70 or Creaton CA06/H-Judd), these are the fastest in the game. The only track available in this discipline is Le Mans.
Start the race and take it easy in the first few corners. After about 1.2 miles you will get onto the first long straight, put the pedal to the metal and you will be driving 200mph in no time.
Can be done in GRID World (career), Race Day (single player) and multiplayer.

During a race perform a full spin and win the race. You will at some point during a race spin out and make a full turn, the only thing left then is to get back to the front of the pack. If you want to do it an easy way, start a race from Race Day and put the difficulty to Basic, this way you will not have to many trouble catching up with the leader of the race. Make sure you set the lap count high enough to enable yourself to recover. A minimum of five laps to be safe is recommended.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

You have to win an event without touching any of the other cars. This is not just winning a race, but an entire event, that can consist of multiple races. Drift and Touge discplines do not count for this achievement and neither do the Head 2 Head and Le Mans races.
The easiest way to get this achievement is to choose the Pro Tuned Dunlop Spa Challenge in the Euro R License. This event consists of one three lap race on the circuit of Spa Francorchamps. This is a wide track and because it is a one race event the chances of bumping into another car are lower than with a full blown multi race event.
Set the difficulty to Basic and start the race. During the race, take it easy and overtake the competition one car at a time. The three laps will cost you about 6 - 6,5 minutes so there is plenty of time. Use a flashback if you happen to make contact with another car.
Can only be done in GRID World (career).

In a race, cross the finish line in reverse, finishing in first place. To pull this off you need to have a solid lead of at least five seconds. I would recommend a lead of at least ten seconds to be hundred percent safe. Just before the finish line press to use the handbrake and flip the either left or right to make a turn of 180 degrees. After you have completed your turn use to switch into reverse gear and drive across the finish line in reverse.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

After you accumulate your first €60.000 in your career you will be able to race with your own car. This will also open up the ability to acquire sponsors. You have a total of eight sponsor slots on your car. After you win an event you will acquire three new sponsors. To put the sponsor decal on your car and fill a sponsor slot in GRID World (career) go to ‘My Team’, ‘Sponsors’ and then select a sponsor for the slot. Fill all eight slots to acquire the achievement.

After you acquire €60.000 in your career, you will be able to enter races with your own team and car. This will not count as the first car you buy, since it was already in your garage and the €60.000 was used to restore it. After you win a few events you will have enough money to buy a new car. The cheapest car available is the Jupiter Eagleray MK5. This is a Demoliton Derby car and it costs €21.000 new and is available from €16.500 on eBay Motors. Enter the Michigan Demolition Derby on your ARL Rookie Badge to be able to purchase this car.
Can only be done in GRID World (career).

There are 43 cars available in the game in total. See this spreadsheet for a checklist of all cars. The only car that is not buyable in GRID World (career) is the Porsche 911 GT3 RSR, this car can be driven in the first few Le Mans races in GRID World (career) as a 'Driver Offer'. It is also available in Race Day (single race), in the Le Mans Series and 24 Hours Of Le Mans disciplines.
Cars driven are accumulated over GRID World (career), Race Day (single race) and multiplayer.

In the career mode you will be able to enter events and each event features between one and five races. Win all of the races in one event. This achievement will be easily unlocked while going through the career mode.
Can only be done in GRID World (career).

Unlike you would expect it is not about you winning an event for your team. Each event also has a team ranking, based on the points the team's drivers gather throughout the races of the event. Be on top of this leaderboard at the end of the event. It will be very easy once you unlock the ability to use a team mate (after unlocking the second license in any region) and hire a good team mate. To do this before you get a team mate, go to the Pro Touge Champion Touge Shield in the J-Speed Rookie license. Win this event and your team will also be on top of the leaderboard, because there is only one team with two cars in this event and they don't perform well enough to top the team leaderboard.
Can only be done in GRID World (career).

Win a race to unlock this achievement, couldn't be more simple.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

In total there are 51 trophies in GRID World (career), they are divided into ten licences:
ARL Rookie Badge - 6 events
ARL Pro Badge - 6 events
ARL National Badge - 3 events
Euro R License - 6 events
Euro B License - 6 events
Euro A License - 3 events
J-Speed Rookie - 6 events
J-Speed Super Two - 6 events
J-Speed Super One - 3 events
Global Racing League - 6 events
Can only be done in GRID World (career)

This achievement can only be unlocked when driving in GRID World (career). If you improve a lap record, you will see ‘WR’ behind the lap time. Unfortunately, you cannot see the lap record of a track in GRID World. If you want to know the lap record for a specific track, select it in Race Day (single race). There is not really a need to select a specific track you want to set a lap record one, since you will most likely break numerous lap records during your career.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

In total, there are fifteen locations in the game, complete a race in all of them. The fifteen locations are:
San Francisco –ARL League
Washington –ARL League
Detroit –ARL League
Long Beach –ARL League
Milan – Euro League
Jarama - Euro League
Istanbul Park - Euro League
Spa Francorchamps - Euro League
Donington Park - Euro League
Nürburgring - Euro League
Le Mans - Euro League
Yokohama – J-Speed League
Shibuya – J-Speed League
Mount Haruna - J-Speed League
Okutama - J-Speed League
In the career all these locations, but Shibuya and Le Mans, are available in the first license category. Shibuya is available in the second J-Speed license events, while Le Mans is the decor of the 24 Hour of Le Mans race at the end of each season (a season lasts four events).
Can be done in GRID World (career), Race Day (single race) and multiplayer).

When you start your career you will only be able to race for other teams. Every time you will have three races to choose from. The top one is the North American ARL League, the middle one is the European Euro League and the bottom one is the Japanese J-Speed League. Race for a team in each of these.
Can only be done in GRID World (career).

You have to win a Le Mans 24 Hour race on Pro Mode, meaning that you cannot use any Flashbacks or restarts during the race. Winning does not necessarily mean that you have to get first place in the race, as long as you win your class.
To make it easy for yourself put the difficulty to Basic before the race. Do not forget to select the Pro Mode as 'On' in the same screen. During the race be careful, brake on time, don't overshoot any corners or bash into walls. The hardest part are the ten hours (five minutes) in which it is dark, this makes it a lot harder to drive, especially in the very shallow corners on the long stretches. It is probably best to drive a few practice laps before you attempt this achievement, track knowledge will give you an advantage. If you would be involved in such a heavy crash that you are not able to win the race anymore, quit to the Dashboard and restart the game, or wait untill the next season for another chance.
Can only be done in GRID World (career).

After unlocking a license in the second category (ARL Pro Badge, Euro B License or J-Speed Super Two) your garage will be expanded. This will give you the opportunity to hire a teammate. At first you will be given a choice of three drivers to hire. From then on you can hire other drivers. To hire a driver go to ‘My Team’ in the GRID World menu, then ‘Team Mate’ and press to fire your current teammate and hire a new one. Look for a driver that has better skills than the current driver and hire him.
Can only be done in GRID World (career).

After each season (each season lasts four events) there will be the opportunity to race at the Le Mans 24 hour race. You will automatically see it pop up when you select ‘Race Events’ from the GRID World menu when the time is there. For this achievement you need to simply complete the race, no matter in what position, what the state of your car is at the end of the race or whether you are driving for your own or another team. The timer is set at 24 minutes, but it is actually just 12 minutes of racing. You can also do this by firing up a 24 Hours Of Le Mans race in Race Day (single race).
Can be done in GRID World (career) and Race Day (single race).

Every event in the career mode has a Hall of Fame, this leaderboard shows the five drivers with the most victories in that specific event. These drivers are fictional and their wins will not go up. In order to get onto the leaderboard you have to equal the amount of wins of the nr. 5 on the leaderboard.
The easiest leaderboard to get on is the Classic Muscle Bilstein Festival Milano in the Euro League. This event is on the bottom left of the Euro R License events and is available without having to buy an extra car.
The nr. 5 on the leaderboard has two victories, so you will have to win the event twice to get onto the leaderboard. The event itself has two races.
Can only be done in GRID World (career).

Refer to "Five Xbox Live Wins".

Go online and win five ranked matches, simple as that. There is no real system to have an easy race, given the voting system in GRID. But you can get the achievement pretty easily by racing focused and trying to avoid the onslaught in the first corner.
Can only be done in ranked multiplayer.

Refer to "Long Haul".

Drive 1000 miles. You will most likely attain this when you are almost through the career, if you don't do a lot of single races/multiplayer. If you want to get it quick, don’t skip the Le Mans races at the end of each season, these add about 20-30 miles to your total within one race.
Miles driven are accumulated over GRID World (career), Race Day (single race) and multiplayer.

This achievement is similar to 'Short Haul' and 'Long Haul' but this time you have to drive the 750 miles with just one car. A good option is the Audi R10 TDI, purchase this as early on as possible and do your Le Mans races with it. This way you will build up a nice amount of miles while completing GRID World (career). Once you have completed the career, you can do Race Day (single race) races with the car, use it as much as possible online or redo career events. This way the achievement should come with little pain.
Miles driven are accumulated over GRID World (career), Race Day (single race) and multiplayer.

The Driver Leaderboard is comprised of the 500 top drivers based on the total reputation they have gained. As a rookie you start at the bottom and you need to work your way up to nr. 1. The nr. 1 on the leaderboard has about 4,000,000 reputation points. If you finish the whole career on 'Normal' difficulty, with automatic gears, all assists on, 'Pro Mode' & 'Force Head Cam' off, you will easily have more than 5,000,000 reputation points at the end of your career.
Can only be done in GRID World (career).

The Team Leaderboard is comprised of the top teams in GRID based on the season earnings. Every season all teams start at $0 and the team that earns the most money throughout the season will top the Team Leaderboard. The nr. 1 (Ravenwest) earns about $14,000,000 per event. This may sound like a lot of money, but is easy achievable towards the end of your career. When you have unlocked the Global License, have good paying sponsors and a skilled team mate you can easily earn $18,000,000 per event. The achievement itself will unlock as soon as you hit the nr. 1 spot on the leaderboard, even if it is only one event into the season.
Can only be done in GRID World (career).

A new Lamborgini Murcielago GTR costs $2,100,000. You will need to have a balance in the career of $2,100,000 to unlock the achievement, so this has nothing to do with earnings, just with your current balance. When you start getting more sponsors and winning more races and events you will get this really quickly.
Can only be done in GRID World (career).

To sell a car for more than you paid for, you have to put it up on eBay Motors, selling it directly will always give you a lower price than the price you bought it for.
It is wise to have this achievement in the back of your mind when first purchasing a car. Get one of eBay Motors that has a lot of victories and little terminal damages, after winning a few races put it up on eBay Motors for sale. Set the starting price at about 33% of the price for a new car, put the buy now price about 20%-25% higher than the price for a new car and let the auction last four events.
After each event you will get a bid update. Usually after the first event the bid price will be about 66% of the new price, after three events you will likely reach the new price and after the fourth event the bid will be somewhere between the new price and buy now price. This means you have sold it for more than you bought it for.
Can only be done in GRID World (career).

This is a viral achievement, that means it is not very hard to get. Beat someone that already has the achievement, you do not have to win the race for it to unlock, just finish higher than someone that has the achievement.
Can only be done in ranked multiplayer.

After you complete all events from a license in your career you will be challenged by your big rival, the Ravenwest team. You will race a head to head race against one of their drivers and you need to win to get the achievement.
Can only be done in GRID World (career).

Set up a Demolition Derby race in Race Day (single race) and put it on somewhere between 30 and 50 laps. The long track will take about 35 seconds to complete one lap, so even with 50 laps you can complete the race within half an hour. For the first 20 laps just race. During these laps more and more competitors will roll onto their roof or crash into a wall. After about 20 to 30 laps, only three other competitors will still be racing, they will not crash, unless you take them out. Start driving close to them and once they are about to jump over one of the ramps, hit them in the side of their cars. This will cause them to spin and roll of the ramp, immobilizing them. Take out all three of the remaining cars to be the last survivor.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

Touge is head to head racing on narrow mountain roads. There are two variants, the Pro Touge, which consists of two races, one downhill, one uphill, and there is Midnight Touge, which is just one race. To unlock the achievement, you have to win a Pro Touge or Midnight Touge on 5 star (Extreme) difficulty.
This may seem hard, but there is one track on which this can be accomplished relatively easy. In Race Day (single race), select Pro Touge as Discipline, the Nissan Skyline as the Car, Mount Haruna as the Location and Foothills as the Route. Set the Grid position to Front and start the race.
If you are familiar with the track you can easily build up a four second margin during the first heat and you only have to follow your opponent in the second heat. So make sure you have either practised the track a few times or you may already know it from the career where it is the premier Touge route.
Can be done in GRID World (career) and Race Day (single race).

Plough your car into the wall to see the screen go red and the image into slow motion. You have caused terminal damage to your car and unlock the achievement.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

The Flashback feature lets you ‘go back in time’, not too much, but just enough to undo a nasty crash. From a race (when you have not just experienced a fatal crash), there are two ways to initiate ‘Instant Replay’ (the first step to using a Flashback). The first way is by hitting the button, the second way is to press to enter the pause menu and then select ‘Instant Replay’. A fatal crash will automatically initiate ‘Instant Replay’.
After you have initiated ‘Instant Replay’ use and to rewind and fast forward to the point where you want to resume the race. When you have found this point press the button to use a Flashback.
After using the Flashback cross the finish line in first place to unlock the achievement. You do not have to get involved in a major crash or spin of the track to be able to use a Flashback, you can do it at any moment of the race, even just before crossing the finish line.
Can be done in GRID World (career) and Race Day (single race).

To earn the full reputation available in a race, you have to have the following settings:
Difficulty - Extreme (even if you have unlocked Ninja difficulty, Extreme is high enough)
Pro Mode - On
Locked to Head Camera - On
Traction Control - Off
Transmission - Manual
Braking Assist - Off
Stability Control - Off
Also, you have to win the race to get the maximum reputation available.

There are two ways to do this in a relatively easy way. The first is to start a drift event and win that. If you are good at drifting it shouldn't be too much trouble

The second one is by starting a Touge event. This method basically revolves around trapping your opponent by backing into them. When in the event, you have to bare in mind this will be a bit more difficult to reverse into your opponent (but still possible). You will have to get used to the head camera, learn to use gears for reversing and NO RESTARTS. If you mess up, you have to exit out and back in.

Use to shift gear down, to shift gear up. When on the starting line, I found driving off a bit and then reversing worked best whilst holding to see where the opponent was. Best to try and trap them into a corner; sometimes they may get away, so be sure to adjust your steering.

Sometimes the opponent gets stuck somewhere (or roll through a gap in the railings) and he won't move. If this happens, you have probably saved yourself from doing a second round with that opponent (as their vehicle is damaged).

Credits to Thorpe for the last method.

For every race you complete you will receive a certain number of reputation points. Finishing the race will give you at least one XP point and you get one extra XP point for every person you beat. So if you finish in 4th and you have four people behind you, you receive 5XP. If you quit early or wreck your car you will get no points, but neither will there be a deduction of points for quitting or wrecking.
To get to the rank of Legend you will need a total of 2,000 points, before getting to the Legend rank, you will first get the Elite rank at 1,200 points. An overview of all ranks in multiplayer can be found here.
Can only be done in ranked multiplayer.

To unlock the Global License in GRID World (career) you will need a reputation of 1,000,000. You do not need to have all the other licenses unlocked to unlock the Global License, any license that is not unlocked when getting the Global License will unlock upon getting the Global License.
Can only be done in GRID World (career).

Refer to "Online Legend".

The Okatama Grand Circuit is a tricky circuit to master. There are many winding, high-speed turns, height differences and blind corners. To race on this track without any opponents go to GRID World (career), select 'View Cars' and get the Audi R10 TDI. The Audi R10 TDI is the car with which a time under 1:30 is easiest achieved. If you do not have it your garage yet, buy it before a Le Mans or Prototype race, it costs $15,000,000 when buying it new.
Take enough time to master the track, one section at the time, in the end it should be possible to drive under 1:30.
Can only be done in GRID World (career).

After you first start up the game and fill out your personal details, you can choose to go into GRID World (career), Race Day (single race) and multiplayer. In the career you will be thrown into a race directly, in single race you get to choose the track, cars, etc. Start the race and finish it to unlock the achievement.
Can be done in GRID World (career), Race Day (single race) and multiplayer.

Refer to 'Combo King' for tips on how to maintain your combo. To get this achievement you need to use the Honda S-2000, as this is the only 8 Ball drift car. As soon as you hit the 99x multiplier you will get the achievement. This can be done in GRID World (career), Race Day (single race) and multiplayer.

The easiest way to rack up miles is to either play a lot online with one of the 8 Ball cars, or to do laps on the Circuit de la Sarthe 1968 in Race Day (single race). 250 miles is about 30 laps on the Circuit de la Sarthe 1968 and can be done in 1.30 hours with the McLaren F1 GT. For a complete overview of 8 Ball cars refer to 'Jack of All Trades'.

Miles driven are accumulated over Race Day (single race) and multiplayer.

Refer to 'Gentleman Driver' for some tips on how to race a clean race. The easiest way to get this achievement is start a race in Race Day (single race). Set the grid position to back and difficulty to basic. Put the lap count at somewhere between three and five to give yourself enough time to overtake the competition without crashing into them. Also, choose a wide track, like Spa or Istanbul Park. You don't have to worry about hitting walls, because only hitting cars will affect the achievement. For an overview of 8 Ball cars refer to 'Jack of All Trades'.

Can be done in Race Day (single race) and multiplayer.

There are 8 cars in the 8 Ball Pack. They can all be found in at least two events in multiplayer. In this spreadsheet there is an overview of the cars followed by the events it can be raced in. When looking for a race, or setting one up, make sure that the 8 Ball Pack is turned on, otherwise you won't be able to use 8 Ball cars.

Can only be done in ranked multiplayer.