Play as Onslaught:
Beat the game with Ryu without losing a round and you should get Onslaught. He appears under Wolverine.

Play as Shadow Lady:
Beat the game with Chun-li and you should get Shadow Lady. She appears under Gambit.

Play as Mega War Machine:
Beat the game with War Machine and you should get Mega War Machine. He appears Zangief.

Play as Orange Hulk:
Beat the game with Hulk and you should get Orange Hulk. He appears above Ryu.

Play as Roll:
Beat the game with Mega Man and you should get Roll. She appears beside Mega Man.

Play As Hyper Venom:
Beat the game with Venom and you should get Hyper Venom. He appears above Chun-Li.

Play as Lilith:
Beat the game with Morigan and you should get Lilith. He appears under war Machine.

Shadow as a Tag Partner:
After beating the game with Chun-Li or Shadow Lady, highlight Iceman and press down at the character selection screen.

Sentinel as Tag-Partner:
Beat the game as Onslaught, and Sentinel appears under Colossus in the Special Partner screen.

Hints

Thanks to Revolution readers MaN i'm StranG, Alexander Lips, Jereme Hiestand and Jason Allen!