Finish the level while holding a weapon dropped by the enemy. When you start a new level the weapon will be in your inventory.
Custom weapon for each character
Beat every mission in the single player story. Each weapon that you unlock can be then used by the other characters, and there is a custom weapon for every character in the game.
Tachikoma Mini- game and Movie Viewer
Beat the game with any character and unlock a mini-game featuring Tachikoma. There's also a Movie Viewer that lets you watch game's cut-scenes.
Various Dual Handguns
Start a mission with just the handgun. When you get to the end of the mission you'll see it in the other hand. You can equip it again, and it will only take one weapon slot.