There are many different story paths for your characters within the game for you to follow. Here is how to unlock them:

Asley: All you'll need to do for this one is 'taunt' Coyori.
Cedric: During the fight against Marco you need to adjust your glasses 5 times.
Coyori: Try to throw Freed on five different occasions.
Deathbringer: Make sure the killing blow on Watson is Final Inferno.
Dokurod: Once Coyori is down taunt him.
Donvalve: Finish Coyori with a Super and use "hip-de-hop" at some point during the encounter.
Face: At five different points in the fight use Texas Knee versus Urs.
Freed: Hit Marco with Magnum Jetter five times.
Marco: Deliver the final blow on Olivia using Dyna Rush
Olivia: Squeeze in 10 (ten) D attack's on Coyori and use one to finish him off.
Urs: Beat Olivia by timeout.
Watson: Use Hip-de-bunny as the final blow vs Cedric.