By completing various tasks in the game you'll receive fragments on an 'X' mark on the Title Screen (similar to the Bonus Panels found in the stages). Collecting all four fragments will unlock VS Missions, where you can battle each of the game's bosses individually, without any stage beforehand.

Unlockable	How to unlock
1st 'X' fragment	Clear the main game
2nd 'X' fragment	Collect all of the Bonus Panels
3rd 'X' fragment	Clear Boss Rush
4th 'X' fragment	Clear every stage in Score Attack mode (including Boss Rush)