Successfully complete the game on any difficulty setting. Save the game after the credits complete. Reload the saved game to start with a new double dagger weapon in addition to your original two weapons at their levels in the previous game.
Play level 1 and go through the subway when you need to get both Legacy Drives for the Lightning Rod. When you get out on the other side, go into the alley that has the fence with a junkyard on the other side. Walk up to the fence. Press Triangle when equipped with the Lightning Rod and quickly change to your hands to grab on to the top of the fence. Jump over to the other side, then go to the wall that has the ladder on it. Climb up the ladder and get up to the top of the building. Once there, you will find a piece of paper hovering above the ground. Walk into that paper. A message stating that survival mode has been unlocked will appear. Save the game, then enter the bonus option at the main menu to access the new option.
Play the China-town level after getting the Katar. Climb up the Chinese house that has the huge flame on the porch. When you are up there, someone will surprise attack. Kill him and go to the opposite side of the part you climbed up to. Go to the back of the house, but stay on the balcony. Jump to the building on the far side (all the way down, as far as you can see) and look around for another piece of paper. Walk into it, and you will unlock the 3 minute battle mode option.