The easiest way to get this achievement is to play the Big Trouble Little Zombie minigame. It takes minimal effort and I got the achievement on my first try without even going for it.
In the Big Trouble Little Zombie minigame, you'll be playing in a pool level with mini zombies. The conveyor belt will give you lots of Cherry Bombs, Peashooters, Walnuts, and Lily Pads, so just play as you normally would (using the Peashooters to fend off the horde, the Walnuts as your main line of defense, and Cherry Bombs if necessary). After a wave or so, your backyard should be pretty streamlined to take on all of the mini zombies. At the second wave mark, you should start getting more and more zombies, allowing you to plant your Cherry Bombs with ease. There should be more than a few opportunities for you to blast 10 zombies, so if you don't get it right away, try again. This achievement unlocks immediately, so you'll know if you blasted 10 zombies or not. Hope this helps.