Hey everybody!
What you need to do for this achievement to pop you can see in its description. I merely want to show you a shortcut, so you won't play the game and hunt thise little imps, guessing when you'll see the right one for the achievement.
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Go to your multiplayer portal, enter the options panel, choose Private Play. Choose any game mode. Now, where you see "Team Setup", scroll zombie team options until you hit "Zombies : Z7 Invasion".
Guess what : every enemy will be a Z7 imp. All you need to do is start the match and kill one. The achievement pops immediately after the vanquish.
Hope this helps! Game on!