Begin game play in "Nightmare" mode. Reach Electro's level and collect the key. Jump down the left side of the screen and land on top of the Game Gear icon. Return to Peter's room to access an option to start the mini-game.
Wear Venom's suit:
Begin game play in "Nightmare" mode. Defeat the Lizard at the end of level 2, then move to the right and fall into the pit to find the Lizard's key. Walk through the sewage to the bottom of the ladder. Then, hold Down and press 2 to have Spider-Man dive into the sewage. Press 2again, and Spider-Man will appear with Venom's suit.