All these other solutions are fine if you are having trouble actually getting this achievement, but a REAL simple way that requires no actual work to setup, is in the Lady Boyle's Last Party level (with high chaos), from the start of the level, go across the bridge (that you see the Tallboy kill those people on) and go to the right. It helps to have Dark Sight, but isn't needed.
Sneak into the last building on the right, and just after the first door where you enter to the stairs, there will be what looks like 4 Weepers all standing in a circle. Lean around the door jam, prime a grenade (by holding the button until the last two sides), and toss it in the center of the circle. There are actually more weepers than just the 4 here (hidden behind the others), so this achievement popped for me as soon as the grenade hit.
Oh, and there is one Weeper that will walk up the stairs as soon as you come in the building. Obviously don't get seem by him as all the others will run at you as well, but he wasn't included in the 6 when the bomb went off.
Hopefully this wasn't a fluke, and for those of you who don't want to go through a long and boring setup processes described in the other solutions, hopefully it will work for you as well. I did this on easy difficulty, so I don't know if that helped, but it shouldn't matter as it is a grenade, and they are weepers.