Despite playing a lot of Toejam & Earl, I was never actually able to finish off the game. Heck, I was never even close. That's why, when I want to see the ending, I pause the game (usually at the beginning to make things way easier)

Then I press

Up + A + B + C, Right + A, Down + B, Left + C

which makes a 'ding' sound, and doesn't appear to do much until you go to the next stage. The next stage will have a ship part on it, collect it and...

Bam! It's the last piece!

Collect it and it's Ending Sequence for you!