This achievement requires you to get at least one kill with every weapon. Unlike Metro 2033 on the Xbox 360, you DO NOT need to get them all in one playthrough, but also requires the new (DLC exclusive on X360) weapons.
Revolver: Given to you during Hunter, commonly found in the Metro
Bastard: Given to you at the Exhibition armory, commonly found in the Metro
Duplet: Given to you during Chase, commonly found in the Metro
Kalash: Can be acquired during from Bourbon's backpack at the start of Dry
Kalash 2012: Can be found in the Nazi base from one of the enemy (campfire near the generator where commissar standing) and at the Polis vendor and in Church
Helsing: Can only be found in Dead City and the vendor in Armory
Tikhar: Can be found in Lost Tunnels and Frontline, uncommonly found in the Metro
VSV: Can be purchased at the vendor in Armory and Defense, you also get one given to you during Black Station
Hellbreath: Only found at the vendors in Armory and Church
Shambler: Can be purchased at the vendor in Market, commonly found late game
Bigun: Can only be purchased at the vendors in Polis and Church
Abzats: Can ONLY be acquired at Vladimir's armory in Church for free
Flamethrower: Automatically obtained at the start of Dark Star, carries over to D6 if not dropped
Trench Knife: Melee weapon, you start with this
Fragmentation Grenades: Can be found commonly from various loot sources or any vendor in the game
Sticky Grenades: Can be found from various loot sources or any vendor in the game
Incendiary Grenades: Can be found from various loot sources or any vendor in the game
Throwing Knives: Can be found from various loot sources such as target boards or any vendor in the game
Info is from the Wikia, if you find dependencies, please let me know and I will update it. I will also be adding details as I go.