Bonus Characters:
Beat Normal Mode with the regular characters to unlock their special counterparts.

Play as Zhou:
Beat Normal Mode with all nine regular characters. Then beat it once more with any regular character.

Play as Kaiya:
Beat Normal Mode with all nine regular characters. Then beat it once more using any bonus character.

Play as Kazane:

Beat Normal Mode with Zhou.

Play as Jelly:
Beat Normal Mode with Kaiya.

Extra Mode:
Enable all 22 characters to unlock an extra mode found on the Main Menu.

Thanks to Revolution readers Chris Porto and Sinus Man!