When you reach the first exit of what appears to be the end of the Adventure 6: Arcade, shoot your gun into the upper right hand corner of the wall. A part of the wall will disappear revealing the secret passage way. If you can't continue on, then try shooting at the wall some more.
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.