Hard mode:
Beat the game on Easy or Normal.

Blackbird Suit:
Beat the game on Easy or Normal to unlock the Blackbird suit. You cannot change moves or upgrade.

Papillon Suit:
Beat the game twice using the same saved game file. You can assign what super moves you want Vanessa to have at each portal and in between missions.

Alternate ending:
Beat the game on Normal to get an different ending from Easy.

Best ending:
Beat the game on Hard and get at least a "Regular" rank overall.

Thanks to Revolution readers Puffy and Maximus44!