The achievement description speaks for itself. Defeat 200 enemies using the Bite which is the
button. What I did personally was from the very start of the game I kept using the bite on all enemies with a few exception where I was ganged up and had to use the boomerangs to thin the herd till there was just one enemy left. For me I got mine on Snow Worries the first ice level in the second hub of levels after the first boss, but yours can pop up in any level.
The most annoying enemy will be the Frill lizards because if you try to bite them, they'll back off and they're usually surrounded by other frills which in turn they gang up on you. But keep press the
button and it will land. If you need to use your boomerangs to have a one-on-one encounter go ahead. Some enemies the kangaroos or the guys with the cricket bats take two bites to finish them off.