Yeah, that's one I want to implement.
Achievement Unlocked: Doing it Wrong

Also to be implemented:
Lose Yourself No Skips (Don't die)

Does anyone have ideas for other achievements?

I would like to throw in some extra stuff to make it worth the extra playthrough. A timer and a scoring system. Maybe include an exit that functions like the one in JJ2's Treasure Hunt mode. Also, a few minor things... Like shortening the title music. The game is 4MB. Half of that is the title song.