Complete all 26 story missions, clear the final Sandman fight and you can play through the second time with the black suit Spider-man.

You can also get it by beating the game and going to the upgrades section on the pause menu. Then go down to playable characters to be Venom, New Goblin, Sandman, Lizard, or Black Suit Spidey.

Submitted by spider-addict (pdonaldson4) on MSN