Pick up any item lying around (Z) and either throw them at enemies (Z) or eat it (X)! You can also pick up and eat enemies, as well as normally dangerous items like bombs. In most situations you must defeat all enemies to continue.
HINTS:
You can eat anything, so do it. It replenishes your health.
I mean anything. Even those bombs in the first boss. And enemies too.
Watch the bosses for patterns, and look for cracks in the walls and the floor.
SUPER HINTS
Dummy boss: Throw bombs on the cracks on the floor
Purple boss: Lure the boss so he dashes into the wall. I think you can figure out what to do from there.