Complete the game and at the end, when prompted, save your game. Then, from the title screen, load your saved data to start a new game with everything you had when you beat the game.
Survival Mode
Complete the game 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.