One simple way to get this achievement is to get this after following one of the solutions for the Animal Mishandler -achievement. (Lose all monkeys in one go)
Anyway, once you find a way for killing all the monkeys in one go, just tap Try Again and Action. Repeat until there are all the 100 kills.
I tried thecatwhowalks's solution (which worked very well, btw!) and then repeated it for less than 20 times until the achievement popped.