Clear every mission in the 1-player story with a character to unlock that character's personal custom weapon. You can get a weapon for every character in the game, and any weapon you unlock can be then used by the other characters as well.
When an enemy drops a weapon that you don't have in your inventory, pick it up, and make sure to finish the level while still holding it. When you start a new level the weapon will be permanently added to your inventory.
Just beat the game with any character in order to unlock a SpyHunter like minigame featuring Tachikoma, and a Movie Viewer that let's you watch all of the game's cutscenes again.
If you start a mission with only a handgun equipped, at the end of the mission you will be rewarded with that same handgun in its dual form - 2 of the same gun that can be equipped at once, only needing 1 weapon slot to hold.
You can use this method to unlock a dual version of each of the standard handguns in the game.