Simply use the Flashback during the Young Driver Test. Hit  to go into the Flasback menu and hit .

You will have to bet all 11 test on the Young Driver Test, including some specific in test to get all 36 chevrons. Just follow the audio queues to get all possible Chevrons at each test. They are:

Day 1:
Car Introduction - 4 Chevrons
Straight Line Test - 2 Chevrons
Racing 101 Video - 1 Chevron
Hairpin Turn Test - 6 Chevrons
Baseline Performance Test - 4 Chevrons
Kers and DRS Video - 1 Chevron

Day 2:
Kers & DRS Systems Check - 3 Chevrons
Kers & DRS Performance Test - 4 Chevrons
Tyre Conservation Video - 1 Chevron
Wet Weather Test - 9 Chevrons
Evaluation Test - 1 Chevron

You will get this when going for "Earning Your Stripes."

You will get this when going for "Earning Your Stripes."

You will get this when going for "Earning Your Stripes."
This will also unlock all cars possible on carrer (Up to Williams).

Go into one shot qualifying while on Season Challenge Mode and place a valid lap. If you cut corners the lap will be invalid. This does not have to be fast, just valid.

If you are doing a carrer or a season challenge on easy (Amateur AI) this should not be challenging. Just make sure you have auto-brake off and this should be a walk in the park.

Self explanatory just finish a race, no matter in what position.

This can be a little tricky. The easiest way is to do it on easy (Amateur AI) while strating as pole (so you leave out the possibility of hitting another car). Use all KERS at the start so you can go past the first turn clean and from then just keep you car off the grass, walls and objects and you will get it. If you are struggling set auto-brake to on so you won´t miss a breaking point and end up on the gravel or grass.

Also self explanatory. Just finish the race on the podium. Again if you are struggling go to easy difficulty.

Probably the hardest achievement on the list. 
For this you will have to turn off all assist, but you can keep the AI difficulty on "Amateur" which really helps..

You will need to turn off:
Braking Assist, ABS, Traction control, Dynamic racing line and Pit Assist.
Also, Gearbox will be need to be set to manual.

I suggest Monza as the easiest circuit as it has the fewer corners and longest straitghts.

Make sure you select the cockpit camera and complete the race. The end position does not matter.
If you are doing a quick race you will be able to select it before going into the car.
If you are doing Season Challenge or Carrer just hit  until you find yourself inside the car.

All other assist can be on, but gears must be set manual. Again I suggest the "Amateur" AI Difficulty on Monza. This can be done on any mode (Quick Race, Season Challenge or Carrer).
Normally you will use  for Gear Up and  for Gear Down.

You will need to finish qualifying on first position. If you are doing this on Season Challenge you will get "One Shot Hero" as well.

You will need to finish the race on first position. The lenght of the race does not matter. If you are doing it on "Amateur" AI this should not be to difficult.

You will get this when you win a race starting from pole. If you manage to do all in one race you should also unlock "Race to Victory" and "Polesitter."

For this you will need to set the fastest lap in a race without penalty (no corner cutting) and make sure it is the fastest of the race. You will get a visual confirmation if you do the fastest lap on the screen a little after crossing the finish line at every lap. If another racer beats your time you will see another warning with the race name and his time. You will have to bet that time before the race ends to get this.

Press clipping are quick texts about the racing world during the season. To get into one you will need to win a race so you will get mentioned. Should not be to difficult and will come normally as you progress through the game.

You will get objectives in terms of qualifying, race finishing position and beat your rival during every race at Season Challenge. When you beat all of these objectives on a single race weekend you will unlock it.

At the begining of the Season Challenge you will need to select a rival. Each rival challenge consist of a best of 3 races. When you win 2 races you will beat the rival and get this to pop!

In order to get this you will need to bet all rivals with 2 races only so you have enough time to get this. While shooting for this also try to get "Back to Your Roots" or "Itchy Feet."

You can either loose all rival challenges or simply decline the contract offers you get when you beat them. All that matters is that you do not change teams.

When you make your first team move select either one of the team members of your former team as your rival. Beat him and accept the contract offer to go back to your original team. This must be done with the team you START your season with.

For this you will need also to win all rival challenges in two races, but unlike "Back to your roots" you will need to select 4 different teams. So it is impossible to get them both at the same season (unless you turn auto-save off).

This should not be difficult if you start on a middle team and work your way up to the top teams beating all objectives and finishing on podiums and winning. Again if you are struggling try setting the AI to "Amatuer" so it can be easy to finish on 1st.
You will get more point on Medium than Easy and more even on Hard. (Hard does not mean hard AI, simply that you start on one of the worst teams), so it might be worth a shoot at Hard if you are close to 25k. I got close to 40k winning all in Hard so there is a lot of room even if you can´t win all races.

See "Hardcore" achievement for further details.

Hard difficulty means you will start the season on either caterham, HRT ot Marussia. Make sure you get out of them as quick as possible and upgrade to better teams quickly so you can win races more easily. You can use AI in "Amateur" so the Hard here is starting from the bottom teams. These will unlock when you achieve enough points to be champion even if it is not the last race (i.e., if it is mathematically impossible for anyone else to overcome your current points).

Scoring the maximum points means winning all races. The fastest way is to go to the "Easy" challenge and select either McLaren, Ferrari or Red Bull. Keep AI in "Amatuer" and win them all!! If you do not have it you will get "Winning Ways."

You will need to set the fastest lap on all 5 events of the long race weekend:
Practice
Q1
Q2
Q3
Race

If you are having problems I suggest THIS SITE for car set-ups that will make your life a lot easy.

This will happen normally from the middle to the end of the season if you are doing well. You are most likely to have contracts from Marussia, HTR, Caterham and also a contract from the rival you beat later on the season. The important here is not to do anything while you don´t have 4 of them. Just keep them waiting for your answer.

This has to be done on Carrer. You will need to finish Q2 and do not move the Q3 so you will start 11th or below. Once the race starts you will need to overtake everybody to finish first.
If you are having issues I suggest:
1. Use THIS SITE for car set-ups that will make your life a lot easy.
2. Setting AI to "Amateur."

Depending on your performance you may get contracts to move to another team mid-season. This will normally be a quick response contract offers (I got one from Mercedes while driving for Force India). Just accept the contract and move to a different team.
I suggest doing this after "On Demand" and also waiting for the second carrer season beacuse it is very unlikely you will get a good team to offer you a 1st driver seat so you can go for "New Direction" and "Cut Your Losses." If you stay with the same team you can also go for "The Equipment may be the Same."

In order to change R&D paths you MUST be the 1st driver. Equal status will not allow you to do it.
To be the first driver you need to beat your teammate at every item on the "teammate challenge". You will get reviewed 2 times - At the end/beggining of each season and at race 10 - Germany. You will need to go from 2nd driver to equal and then to 1st. So it may take a whole season. If you Change teams make sure you will get Equal or 1st driver, or you will need to go an entire season to get 1st driver and be able to do this.

When you are first driver the team will ask you what path you want to take. Change it and after the next Race with and R&D objective (the little gear icon on top of the race name) you should get it.

Same as "New Direction" but you will have to end R&D. Reffer to New Direction for more details.

There are a total of 20 races on a career season. You will have to be pole at 16 of them. Again the major hints are:
1. Use THIS SITE for car set-ups that will make your life a lot easy.
2. Setting AI to "Amateur."

For this you will need to finish in front of your teammate on every qualifying session of the season. Does not matter your starting position, as long as it is in from of your teammate. It is important that you do not change teams mid-season for this achievement. If you do you will need to wait for a new season and complete it all with the same team.

General rules stay the same if you are having problems:
1. Use THIS SITE for car set-ups that will make your life a lot easy.
2. Setting AI to "Amateur."

Unlike F1 2011 this year´s game allows you to change the difficulty, which helps a lot to make this a lot easier. Same principle applies here from Season´s Challenge "Winning Ways." Just to help out, here are the points for each position:

1st - 25
2nd - 18
3rd - 15
4th - 12
5th - 10
6th - 8
7th - 6
8th - 4
9th - 2
10th - 1

Almost impossible to get on your first season unless you win everything and have a decent teammate like Maldonado who will contribute with a couple of points. 
Though it dependes largely on luck on your first season, as you move to your second season and keep winning races you will be offered a contract with a solid team, in which you teammate does help out by putting points on the board. Save the rival challenge at the end of the season for a good team and move to that team so you can get this one.

Go to Proving grounds and select Time Trial. Select a team (Red Bull makes it more easy as it is a good car) and set 5 clean lao times - without any corner cutting at 5 different circuits.
Since you will have all 20 circuits at your dispossal just pick the 5 you are most confortable with and set a lap. It does not matter how fast it is, just that it is clean.

I suggest going for Austin while doing this, beacuse if you beat the time of 1:39.635 in Austin you will also get "Austin Power."

Refer to "Gold Rush."

Again on the Proving Grounds select the Time Attack. There are 6 different circuits: Each circuit will have it´s own gold time to beat as follows:
Valencia: 1:39.871
Silverstone: 1:47.960
Hockenheim: 1:26:119
Suzuka: 1:35.413
New Delhi: 1:29.939
Austin: 1:40.165

Thanks to Maka here is a Thread with videos off all single challenges for time reference.

Champions Mode is one of the new features of F1 2012. For this you will need to beat the first challenge, which is beating Kimi Räikkönen. It does not matter in which difficulty you get this (Easy, Medium or Hard).
Here is a video if you are struggling:

F1 2012 | Champions Mode #1 / Beat Kimi Räikkönen | HD - YouTube

The last scenario will only be unlocked after you progress through all of the first 6 challenges. 

To get a gold medal on any challenge you will need to complete it on Hard difficulty. You can have as many driver assist as you fell like, but I recommend getting Pit Assist and Braking Assist off. Try getting your fuel mix to Rich as quick as possible to get the edge as you will not be able to change set-ups or do much change on the car.
It may take you a couple of tries until you are familiar with the circuits and overtaking positions.

Here is a video of the final scenario being done:

F1 2012 - Champions Mode - The Ultimate Challenge - Part 7 FINAL - YouTube

Refer to "Best of the Best."

Refer to "It Takes To Baby."

Co-op mode must be done over Xbox Live as Split Screen does not allow it.
For this, please reffer to This Thread for a Co-op partner.
You will either need to go through 2 carrer modes so both of you can get this and "Co-op Drivers' World Champion" or you can use the method discribed on the Roadmap by Maka below:

"Both players should trade wins back and forth to keep the points very close to each other. Now, on the last race, have the host quit out, and the other player will finish the race to get the achievement. Once this is done, invite the other player back in, and let the host finish the race in first, making sure to win by enough points to beat the other human player."

Refer to "Online Addiction."

This is by far the most anoying achievement if you do not have a boosting party, simply because on-line gaming of F1 looks like cars on rampage. There is little to any curtesy on online matches and turn one is often a crash extravaganza.
My suggestion: Go to This Thread for a boosting party!

You should get this while going for "Trials FORMULA ONE" so it takes one of the 5 circuits out.
Choose Dry weather and change the set-up of your car to get a faster lap. I recommend using THIS SITE for car set-ups.
Here is a video of this getting done that might help you with the times on each sector:

F1 2012 - Austin Power Achievement/Trophy Guide - YouTube