Medal of Honor

I managed this on the very first mission. Either switch to single shot fire using the D-pad or switch to the pistol. I got the majority of kills when entering the building where you kill the lights and use night vision, they cant see you so dont shoot and dont move! Cheev!

The earliest i managed to get this was in Dorothys Bitch

I did try in earlier missions with a pistol and also tried with shotgun got between 7 and 9 headshots but no achievement. You know when its a headshot kill as a Head silloeutte appear at the bottom middle of the screen with a target over it.

At the beginning of the level you are told how to change weapon fire rate, do this to single shot and proceed only killing if you can get the headshot. Take your time. You can get 1 at the start, then another 1 or 2 at the first small camo then the rest as you head to the artillery gun just to the left of the camp.You will see the gun fire from the rocks aimed at the ac-130. These guys hardly move making them easy headshot targets!! There are more than 7 here total so it doesnt matter if your team kills any. Im not sure what the weapon is called but its the 1 with the scope.

I only used 1 bullet per kill for the 7 and didnt reload the weapon either.

Edit :
Another place that you will probably find easier is on the level Neptunes Net whilst going for your The Quiet Professional achievement this should come hand in hand with that as you need to headshot these guys in order for them not to be alerted,just put your weapon on single shot,make sure to use the scoped assault rifle M14 EBR not pistol

If you are going to vote negatively please leave a comment as to why, so i can make my solutions better

In the very first level, you come to a point where you kill an enemy from behind, just before taking out the MG gunner. This guy drops a Dragunov, which is very easy to get headshots with. After picking it up, you move ahead a little and then you will have to cover Preacher and Voodoo. You can easily get 7 kills right here.

If you are going to vote negative, leave a comment why, so that I can improve on my solution.

Another mission you can get this on is Compromised. Near the end of the mission, you start going downhill. Once you do the buddy boost, and jump off of that roof. You will come across an endless spawn of enemies if you don't activate the next checkpoint. It might be troublesome, but they just keep coming, so you can have limitless attempts at this achievement.

For those of us that aren't good at getting headshots or aiming I found a very easy way.

The last level, Shahikot valley, Objective - Eliminate AQ fighters. You will be behind a rock with a bunch of guys shooting at you from the front and left up the mountain side. Take a sharp left up a hill to a ledge where there is some rocks you can crouch behind. You will see two rocks forming a V shape that is perfect to aim through when crouched. This is best with your scoped weapon on single shot. Find the turret and aim for the head. Hold the L trigger to keep scoped in, don't move the scope at all and in a few seconds another guy will spawn and take the turret. Wait until you see him firing the turret and pull the trigger again. Since the turret isn't mobile they will line their heads up in the exact same spot.

This is an easy Achievement, that I just popped only two minutes into the game.

In the very first mission, at the very start of play when you are escaping from the exploded pick-up truck you are in, you start the mission out with a M4 CQBR - basically an M4 with a red dot scope, and a infrared laser sight.

Just proceed down the alley you are trapped in, making sure to take cover along the way. Line up your headshots with the scope as you encounter each enemy down the alley way, and have at it.

At the end of the alley, there will be at least one tango inside the building to your right, and three tangos on to top of the building across from the alley. By the time you have killed all of them with headshots each, this Achievement will have popped . . . just in time to hit the very first checkpoint on the level.

I got this Achievement in under two minutes of starting the game, playing on HARD difficulty. I did not have to switch to single round fire. However, if you are having a hard time seeing in the dark, you can switch on your NVG (on the D-Pad) and where your infrared laser sight is visible.

Easy peasy.

From x360achievements.org:

For this achievement, all you have to do is kill 7 enemies in a row with headshots. This achievement is quite easy as enemies don't move around much and when they pop up out of cover, they remain there for a while. Press Left D-Pad to switch between firing modes (if your gun has the option), and choose single fire. Then get a headshot. You will know if you killed the guy with a headshot, because a headshot symbol will appear at the bottom of your screen. You can get this achievement in any level. If this achievement is hard for you, play on Easy. If you are still having trouble with this achievement, then play Mission 9 "Neptune's Net". You can silently kill 7 people in a row with headshots, without alerting anyone, and without your enemies firing back.

Note: You can use sniper rifles such as the Dragunov SVD, but not long range sniping rifles such as the M82. Long range sniping rifles are when you are able to zoom in and out using LS.

Just take your time and go for head shots. This is very easy, even on Hard. If you start to get hit then just back out and regain you health.

Did this on the first mission on Hard.