Play as Hisui:
Beat the game on Easy.

Play as Hotsuma:
Start the game with a memory card containing a saved completed game from Shinobi, and then beat the game on Normal.

Play as Joe Musashi:
Beat 88 missions and get all the Secret Clan Coins.

Alternate Hisui costume:
Get all 88 Secret Clan Coins. Alternate Hibana costumes:
Beat the game on Normal or Hard.

Thanks to Revolution readers Johnson and andre3000!