Unlock the following modes by performing the corresponding tasks:

Stage mode
Complete a stage in Arcade mode under Normal setting to unlock it at the "Extra" menu. You can then replay that stage as desired.

Endless mode
Complete the game in Arcade mode and all five stages in Stage mode. There are no Bosses in this mode, with the stages cycling endlessly.

Extra mode
Complete Arcade mode. Extra mode will be available after Arcade mode is selected again. It features a higher difficulty.