There are three extra battles available to you in Original Mode, depending on the character you select. Finish every stage with either a Meteo Combo, Meteo Tag Combo, or Character Parade to unlock the respective hidden battle:

vs. Kairi: Hokuto or Nanase
vs. Shadow Geist: Skullomania or Sharon
vs. Evil Ryu: Sagat, Ken, Sakura, and Vega or Vega II