For people who don't know how to play the 4th boss:
Once you unlock enough songs you'll see a purple skull highlight a song in your selection, play 3 of those highlighted songs in a row (without quitting) and then on the forth highlighted song, you will fight the 4th boss.
When you complete one of those highlighted songs, a purple ball will appear in the bottom right of the song select screen.
 "SCGMD4"){kind=icon}
 "Red Remover Player Pack 2"){kind=icon}
 "Super Crazy Button Maniac Deluxe"){kind=icon}
 "Factory Balls"){kind=icon}
 "Sonic Speed Spotter"){kind=icon}
 "Factory Balls 2"){kind=icon}
 "The Classroom 2"){kind=icon}