You will need to get 10 adrenaline kills during Mission 6: Tashgar. An adrenaline kill happens when you get a kill with less than 30 health, while your screen is bloodshot.
I recommend doing this a shotgun, and you may also have more luck if you play on an easier difficulty, although the video is on hard. You'll want to sneak up behind enemies that are alone in a building or behind cover. Let them see you and begin shooting you. Make sure you are close to them and are aiming at them. As soon as you lose enough health, and see that you're in the red, use your shotgun to kill them immediately. This method also works well with grenades, and even with C4 against tanks.
There are a decent amount of enemies during this level, so just continue to use this method through the checkpoints until you get the achievement/trophy.