Complete the indicated Chapter in Adventure mode to unlock the corresponding character in the other modes.
Draco-Centauros and Witch: Chapter 5.
Ecolo and X: Chapter 7.
Lemres and Satan: Chapter 6.
Schezo and Feli: Chapter 4.
Everything permanently
On the title screen, hold L1 and R1. While doing that, press these buttons in the following order: Up, Down, Right, Left, Triangle, Cross, Square, Square. A doorbell sound should be made if everything gets unlocked.