Crystal is the prize that you will get with medal. You can buy it by money too. Also you can get in from Receive bonus, some EX Medals and 50 by inviting/being invited to the game and inserting the Invitation Code, with a limit of 20 invites per player.
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Crystal used for buying witches, unlock stage without play, power up, rewind and summon Flare. Also in latest updated, you can use it instead MP for upgrade and summon too.