To perform a counter kill you have to knock down an enemy’s health until they’re blinking red. Once there, wait until they attack and you see a red exclamation mark over their head. When you see it press the and you’ll perform a counter move. This is cumulative and can be done in story mode and survival. Must be done against enemies carrying a machete, otherwise it will not count.
A good place to grind these out is about halfway through level 3. You'll come to a point where there's a guy trying to squish you with a boat. You have to kill him before moving on so you can just keep performing counters on the enemies that jump in until you unlock the achievement.