Cheat mode
From the Main Menu enter the options menu (4th option) From there hold the plus and minus button, it should then automatically enter the config menu. While still holding the plus and minus button highlight the Chain Animation option (4th option) then press up, down, left, right. If done it correctly you'll hear a chime and you'll have all modes, characters and the entire gallery unlocked. If using a GameCube controller, go to Options, select configure, highlight Chain Animation and hold X+Y and press Up/Down/Left/Right.
Puyo Puyo! Novolanker
To unlock this you first must have an S rank for all characters in story mode next in the school do 300 Puyo drills after you do these requirements go to options and a new option appears in the options section select that and a new minigame appears called Puyo Puyo! Novolanker select that and you will play it.