To unlock this achievement, you must kill a Carnifex in the same turn that you find it.
In Act IV part 4 (Hunted), you face a Carnifex very close to your starting position. This is the first one in the game.
On Normal, a Carnifex has 4000HP. Using a decent Plasma Cannon you can kill it in a single shot with a critical hit. I used the Mastercrafted variant (Rank II) on a unit with Crack Shot. Have the rest of your squad use an Auspex to boost your critical rate, move someone one square ahead to trigger the Carnifex cutscene, then use the Overcharge ability to shoot the Carnifex. My marine does 3920-4020 damage on a crit.
If you don't hit the damage threshold, you'll have to either quit the mission (lose all marine XP) or finish the mission (kill the Carnifex then run to the end zone, ignoring other units) to retry.
This is also a decent way to level up your Heavy marines (and grind RP), as the Carnifex gives 1000XP to the marine that kills it and the mission is very short.