You need to kill enemies with all handguns, long guns, and gold weapons to unlock this trophy. If you wait until you’ve completed the game, you can unlock all guns and select them from the weapon select menu. You can also track which ones you’ve used in the statistics menu.
There are only 2 weapons that you cannot use via weapon select. The first is a mounted turret, which you can find in various places throughout the game, and the second is a heavy machine gun that you can take from an armoured enemy in chapter 7.