I'm not yet sure what unlocks new characters, but since no guide exists, I thought I would offer some speculation. I unlocked my final character after surpassing 150 gold orbs, many of which I "earned" by completing challenges in versus modes locally with an extra controller. The list of challenges and your progress can be found by selecting the "Gold Orbs" box in the upper-right of the screen below your username.
After having all characters, it's as simple as playing once with each and using its unleash ability.
Characters: Harpoon, Shock, Medic, Piranha, Mooba Mech, Babyfish, Harpoon Drones, Bomb Drone, Slow Mo, Hyper, Aqua Tank, Vortex