Complete the tutorial, then enter one of the following codes at the main menu to activate the corresponding cheat function.

Negative Zone suit
Press Left, Right(2), Down, Right, Down, Up, Left at the main menu.

Iron Spider-Man suit
Press Up, Right(3), Left(3), Down, Up at the main menu.

Scarlet Spider-Man suit
Press Right, Up, Left, Right, Up, Left, Right, Up, Left, Right at the main menu.