I'm pretty certain that this achievement unlocked for me before I used all of the weapons, as I know that I received it prior to level 5 however that is the first level in which you can use the TT-33 gun. If you don't wish to use a list for this one, just pick up every new gun that you find and use it to kill at least one enemy.
Mission 1 Weapons:
SAP9, SM5, Knife (kill move), Grenade, AK74, OTS-02, PECHENEG, Type 97-1, Dragunov
Mission 3 Weapons:
SPAS 12, AR 4, GM-94
Mission 5 Weapons:
TT-33