Fight Ryougi Shiki in Arcade Mode
To fight Ryougi Shiki, win at least four matches before the eighth with Perfects and without losing a match. She'll fight you after the seventh match.
Play as Archetype: Earth in her Crescent Moon Style
First you need to play as Archetype: Earth in her Eclipse Style. Then select her again by using the random character option. When you finally select her she will be in her Crescent Moon Style. Archetype: Earth in her Crescent Moon Style appears to be a phototype or a beta character.