Thanks! Sorry if instructions were a bit unclear/lacking. Guess I ran out of time.
The final boss dies when it touches the lava walls just outside of the stage.
There's two ways to do this, one of them being: finish the levels fast enough so you can eat enough food to get bigger than him. That way, you can knock him off the stage.
The other is a secret! Gasp! It's pretty simple though so don't overthink it.