Clear Special Missions 1-6 in order to unlock the Boss Rush, where you'll face each of the game's bosses back-to-back.
Special Missions 1-6
Clear the final stage of the game to unlock Special Missions. These stages are half the length of a normal stage, either the 1st or 2nd segment of the main stage they're based on, but the enemy placements have been changed to make them more difficult, and the bosses have been powered up and had their EX Weapon weaknesses removed.
Title Screen 'X' mark and VS Missions
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)
Vs. Bosses
You can fight each boss individually by completing the 4 X peaces on the title screen.