When you complete the following tasks the corresponding character will become unlocked.

Deadpool:
Beat the D.C. Level.

Green Goblin and Venom:
Beat them at the end of Wakanda Act 3.

Hulk:
Collect 5 Gamma Regulators.

Iron Fist:
Choose the Anti-reg side in Act 2.

Jean Grey:
Collect 5 M'Kraan Shards.

Ms. Marvel:
Beat the NYC Level.

Nick Fury:
Beat the game.

Penance:
Defeat him in the portal room to the negative zone.

Songbird:
Choose the Pro-reg side in Act 2.

Thor:
Collect 5 Asgardian Runes.