Nom Nom Nom

Note: If you plant any other plant, this will not be achieved.

Strategy
The best way to get this achievement is on Level 1-8 which there are only Zombie, Conehead Zombie and Buckethead Zombie, as they will be the same because Chomper is the only offensive plant you use.

Pick the Sunflower, Wall-nut and Chomper (you have 6 slots, so pick any other plant, but do not plant them). As the achievement states, you can only use 3 types of plants to win. If you plant another plant, you can't achieve this, so it isn't very different from any other -8 level, so it can be beaten easily. When it says "A huge wave of zombies is approaching", don't plant a Cherry Bomb, or you won't unlock this achievement.

Another way to easily unlock this achievement is to not use Pumpkins or Cherry Bombs on level 5-5.

Trivia

 * The Chomper's head on the icon seems to be mishapen.