Warning: This solution may contain spoilers conserning the storyline of Enslaved.
Headshot a Demolition mech 20 times.
I found that the best place to do this achievement is in the end of Chapter Three. You will face a Demolishion Mech with Ammo Boxes lying around, and the Boxes respawn! Place yourself over the spawn of the Stun (blue) Ammo and keep firing the Stun Charges at the head of the Demolisher. You will know you hit the head when the Mech is stunned, and the white aim will turn red when you swipe over it's head. Repeat 20 times and 10 new GamerScore will be yours.
Note that you (as said earlier) can get the total of 20 headshots on several Demolition Mechs over several playthroughs.
The Demolition Mech is a heavy-weight Mech with two demolition-ball looking weapons attached to the end of it's arms. You will first face one of these after the cutscene with the Aquarium in the end of Chapter Two.
Video below is by a YouTuber named Achievaholics who has given me the permission to use the video. I do not, in any way, try to take credit for the production of this clip. He did it in Chapter 10 - But note that if you start Chapter 10 from scratch, you will not have more than 2 Plasma Charges to fire by the time you reach the encounter.
You encounter Demolishion Mechs in the end of Chapter 2 and 3, and in the middle of Chapter 10.
Update: I'm getting several people saying that the Stun Charge isn't capable of unlocking the achievement, so save up all your plasma charges untill the end of the chapter. Save before you start the boss sequence and after you've fired all your plasma charges, quit and reload checkpoint. Repeat until you have the achievement.