To get this achievement you have to kill 35 monkeys that show up throughout the game. Luckily these don't have to be 35 different ones. All you have to do is find one in the game, hammer the ball so it rolls over it, quit to main menu, resume the game and repeat until you get the achievement.

There's a place in Pehua - first chapter of the game, where you're introduced with connected buttons (before you lower the spiked floor). I found this place convenient because there are 3 monkeys sitting around buttons, it's close to the checkpoint so you don't lose much time after realoading, and it's around 10 minutes into the game.