This is one of the first achievements you can get in the game, during Mission 1: Chapter 1 the game will prompt you with subtle tutorials, early on in the level an enemy will rush out of a doorway and attack you, the tutorial style of the game will immediately throw you in to counter kill mode, follow the on screen instructions by pressing "B" when prompted to and after a few hits the enemy will die and the achievement will be yours!
If for whatever reason you mess this up, don't sweat it, just run back up to him and press "B" to initiate the counter kill mode and try again, it's important to note though, this can be done at any point in the game and this is just the first chance you get to do it.
* Credit to RoosterTeeth for the video