Extreme Realism - 10
Recovered from near-death 5 times without dying
A near death experience occurs when you are shot and your HUD turns dark yellow with blood stains around the edges. Once this happens, just take cover as soon as possible or kill the enemy shooting you to allow time to replenish your health. You must do this a total of 5 times without dying in a row. If you play the game normally on hard and take your time, making sure not to die, you are likely to get it without specifically trying for it. Also, you can make yourself seen to an enemy until they shoot you, and then prone behind cover until you get full health back, and repeat that process 5+ times, until the achievement unlocks.
Tier 1 Imports - 15
Got 50 kills while holding enemy weapons
During the campaign, you are able to pick up weapons from killed enemies. Once you kill an enemy, just walk up to their gun, and press , allowing you to pick it up. Now use it until you run out of ammo, getting as many kills as possible. It is not possible to replenish ammo for these using teammates. When you run out of ammo, you will drop the gun automatically and return to your default weapon. Now just rinse and repeat this process for a mission or two, and you should be able to get 50 kills for the achievement.
Peek-a-Boo - 5
Killed an enemy while using peek and lean in the Campaign
See "Lean With It"
Lean With It - 15
Killed 25 enemies while using peek and lean during the Campaign
This achievement should be pretty easy if you focus on "Peek and Lean" kills for a few levels. To preform a proper peek and lean, crouch behind some cover. Now hold and the direction you want your character to move. If done correctly, you will lean out of the cover, looking down the sights. While in this position, you must kill 25 total enemies. Progress saves between levels.
It's Dangerous to go Alone! - 5
Requested ammo from an Ally in the Campaign
See "Lead Farmer"
Lead Farmer - 10
Requested ammo from an Ally 25 times in Campaign
To request ammo, just go up to a teammate, look at him and press . He will replenish your ammo (inlcuding grenade). Just do this a total of 25 times during the campaign to unlock the achievement. Keep in mind that you can't have full ammo while requesting for ammo.
Tactical Toggler - 15
Killed 25 enemies while using Combat Toggle
Some guns have dual scopes (Red Dot + Long Range Rifle Scope). You can toggle between them by clicking while looking down the sights. Just continue to kill enemies with these weapons while using the best scope for the scenario and you should unlock this achievement with natural progression within the first few levels.
The Axeman - 20
Killed 25 enemies with melee during the Campaign
To melee an enemy, click while not aimed down your sights. It is best to kill enemies from behind as it is risky otherwise, especially on higher difficulties. You need to kill 25 total enemies using melee to unlock this achievement. Good missions to boost this if you are having trouble are "Changing Tides" and "Bump in the Night" (Pistol Section).
Unstoppable - 30
Completed Shore Leave on Hardcore difficulty
Hardcore - 80
Completed the campaign on Hardcore difficulty
Your second playthrough will be on the hardest difficulty, Hardcore. This difficulty is not forgiving. It is like hard, but you will have no heads-up display. Also, dieing will restart the entire campaign! But don't worry! Here's where you'll need a USB memory stick. This will be a long and tedious task, but will almost ensure that you get the achievement. Play Hardcore mode as you normally would. Anywhere from 1-3 times per mission, pause the game and back up to the main menu. The game will automatically save your position. Now go to your dashboard and copy your MoH:W save onto your USB memory stick. Now go back into the game, making sure to load it off of your hard drive, and continue to play. If you die, quit out, delete your old hard drive save, and replace it with the one of the USB stick. Just continue doing this until you manage to finish the campaign!
Alternatively, you could try to complete this task legitimately, although it will be quite a challenge. Just try to stay back, never run out, and try to memorize all the big scripted sections.