This achievement can be obtained early in the game with little effort. It doesn't really need a solution, but I suppose one could miss this early opportunity at the achievement.
Hop on the first turret you see in the game. You'll have to avoid enemy fire before you get there. Once you get on the turret, aim for the door as instructed in the game. Once you destroy the door, Watchers will rush out. Just waste them with the turret and you'll easily pop this achievement.
EDIT: The turret seems to be glitched for some gamers, so you may need to get the achievement somewhere else. If you find another good spot to get this achievement, then please write another solution detailing how and where to get it or post in the comments of my solution and I'll post it and give you credit for the find. Remember that we're here to help others out and the more solutions and info we have, the more we help out our fellow gamers. Thanks.
Thanks to Calex dEUS and Subtle Villainy for this information.