New Game + Mode
Beat the game once. Save your game data when asked to. At the title screen, select "Load" and then select the clear game data. You will be at the start of the game with all the status bonuses won from the previous game.

Unlock Survival Mode
Beat the game once on Normal difficulty to unlock Survival Mode

Weapon Select
Follow the same instructions for unlocking "New Game Plus." On the "Katana Select" menu, press L1 and R1 to equip swords to both hands