Complete the game, save, and then load the clear file. Enemies are stronger in this mode.
New Game+
Complete the game, save, and then load the clear file. All your wanzers, character lvls, skills, CP and RP carry over.
Special Machine Gun
Complete Simulator 2.
Special Missile Launcher
Complete Simulator 17.
Various Weapons
There are 20 simulators at all. Some of them won't be unlocked until you beat the last one, and these will give you an extra part or weapon. Note: they are at lvl 1, so be careful to remodel it to its full power.