Hard mode
Successfully complete the game, then hold L when starting a new game.

Jackson
Successfully complete the game in hard mode with an "A" or "S" rank (collect all elves). Start a new game from this saved game to be with all elves including Jackson.

Ultimate mode
Unlock Jackson and start a game. Successfully complete the game using all elves. Hold R when starting a new game to play in ultimate mode.

Easy weapons level-ups
After completing the introductory level where Zero gets his Sword and Pistol, get on the teleporter and teleport back to the base. Immediately exit the place by trying to climb the ladder you are in front of. Ciel will talk to you, and give you several options to select. Keep selecting the first choice she gives you on each option and you will be teleported to a junkyard level. In the middle of the level there will be these pillars that will keep growing back after each segment is destroyed. You can keep destroying the segments with the Sword and Pistol and they will level-up. Keep destroying the segments until the Sword and Pistol are at their maximum levels