From the Option menu, you can change the shape of the Puyos used in most single and multi-player matches. You start with 3 styles (Real, Classic, and Fever) but you can unlock more through story mode by finishing each character's story with an overall S-rank. A special shape is also unlocked through training mode.
Effect - Code
Betanuri - 10 S-ranks
Chalk - Clear all 300 drills in training
Clear - 22 S-ranks
Cube - 15 S-ranks
Moji - 5 S-ranks
Unlock Characters
To unlock 6 new characters, simply beat them in story mode. Each character has a preset order of opponents with the fourth and eighth opponent usually being one of the hidden characters. Beat them and complete the story to unlock them.
Unlock New Modes
There are several new styles of play available in single and multiplayer games. To unlock the new modes, select them in the roulette during story mode. Select a "?" to reveal a new mode. You don't have to win a match in the new mode to unlock it, just select it once and completing story mode. Each opponent's roulette has a preset order of modes. Each new style is only available to certain opponents.