When ever you find an exit in this level don't be fooled, it isn't the end of the game. There is always (except for the last exit #6) another hidden passage to the right of it! When you are in this secret area of the game you find a message (only readable from the map screen) alluding to the zip popping contest.
Press and hold Option 2
Press and hold Option 1 while holding Option 2 down
Move the joypad to the upper right, while holding down both Options
After that, release your fingers, and if desired, turn the music back on. Things behave very strangely in multiplayer mode, so be warned!