EDIT: It seems some achievements only update AFTER completing the mission. You'll need to complete the mission for the mobs to count for the achievement.
In the first area "Creeper Woods" you should be able to find passive mobs. Passive mobs in minecraft (and minecraft dungeons) are mobs that will not attack you (i.e sheep, pigs, cows) Attack these using
or by using arrows (
). You will need to kill 50 of these animals for the achievement to unlock.
These mobs will most of the time drop food and this can help you toward the "Om Nom Nom" achievement.
Note: You can find these passive mobs pretty much everywhere in each level, apart from some areas that don't have animals. The easiest way to get this is to just do creeper woods over and over again.