Alternate costumes
Beat story mode then hold START and press A while selecting the second YOH or the first TAO REN to unlock there alternate costumes.

Onake mode
Complete the game then save the game to unlock.

Shaman king mode
Complete the game then save the game to unlock.

Unlock Asakura Hao
Beat Shaman King Mode with Iron Maiden (Jeanne) as team leader and make Anna's Ambition (Hotel) go to level 5 on that game.

Yoh with Matamune
To unlock Yoh with Matamune you need to beat Survival mode with anyone besides Yoh.

Full powered Hao Asakura
First unlock survival mode then beat survival mode with Yoh Asakura.