Syndicate

As noted in the description, this achievement requires you to perform fifty kills with each of the games weapons, excluding the non-lethal EMP Grenades. This makes a total of 900 kills that can be performed either in the campaign (level select works) or in co-op. Please note however that kill counts aren't updated until reaching a checkpoint. Your stats can be checked from the main menu by selecting Extras > Player Statistics.

Of the eighteen weapons, the UMK MKIV, TAR-39, CQC11, Kusanagi, APP3, Razorback and Bullhammer are available as loadout weapons in co-op.

The Minigun, Thermite, Swarm and LAWS-92 are carried in addition to your other two weapons and will be unable to use ammo crates whilst you have them equipped. In addition to your loadout weapons ammo crates will also provide ammo for the Electron Mace, Gauss and Riotlance. In addition to the loadout weapons, weapon racks may also contain the Minigun, Thermite, Swarm or LAWS-92.

TAR-39 Assault Rifle (TAR-39)
Starting weapon in chapters 4, 5 and 18-20 as well as being found in chapters 2, 3 and 17.

Harbinger G-290 Minigun (MINIGUN)
Found in chapters 5 and 8 (infinite ammo). Carried by Reactive Armours in co-op.

Castellano CQC-11 Combat Shotgun (CQC11)
Starting weapon in chapters 8, 11 and 20 as well as being found in chapters 7, 17 and 19.

RLX-240 Electron Mace (ELECTRON MACE)
The Electron Mace can only be found in co-op where it is carried by Sergeants in Colorado, China and Scandanavia

Coil Laser Rifle (COIL)
Found in chapters 18-20. Also found in Colorado and Scandinavia.

LTB-P Thermite Gun (THERMITE)
Found in chapter 14. In co-op it is carried by Reactive armours, though less commonly than the Minigun.

Razorback M786 Revolver (RAZORBACK)
Starting weapon in chapter 15 as well as being found in chapters 13 and 14.

SEEF-2 Fragmentation Grenade (FRAGMENTATION GRENADE)
To equip Grenades hold Y. Found in chapters 4, 10, 11, 14, 15, 17 and 19. You start all co-op maps with 2 (4 with the Beast Of Burden Chip Upgrade installed). Enemy Grenades can be breached and collected.

APP3 Pistol (APP3)
Found in chapters 1-5, 7, 8, 10, 11, 19.

Swarm Launcher (SWARM)
Found in chapter 10. Can also be found in the weapon lockers in Argentina and New England on Hard or Expert.

UMK Mark IV SMG (UMK MKIV)
Starting weapon in chapters 14 and 15 as well as being found in chapter 13.

Kusanagi HSR-6 Sniper Rifle (SNIPER)
Starting weapon in chapter 14 as well as being found in chapters 3, 4, 13.

LAWS-92 Rocket Launcher (LAWS-92)
Found in campaign chapter 14. Carried by Sergeants across all co-op maps. Guaranteed spawn on the landing pad at the start of the Atlantic Accelerator.

Kusanagi ACR-10 Assault Rifle (KUSANAGI)
Starting weapon in chapters 8, 11 and 18 as well as being found in chapters 1, 7, 10, 17 and 19.

EMW-56 Gauss Gun (GAUSS)
Starting weapon in chapters 4 and 19 as well as being found in chapters 2, 17 and 18. Carried by Sergeants, Liquid Armours and Electric Armours in Northern Territories, Argentina and New England.

Bullhammer Mark II Revolver (BULLHAMMER)
Found in campaign chapters 17 and 19.

Riotlance Dart Launcher (RIOTLANCE)
The Riotlance can only be found in co-op where it is carried by police in China and Scandinavia.

Mjolnir H.O.G. Automatic Shotgun (MJOLNIR)
The Mjolnir can only be found in co-op where it is carried by Sergeants and Liquid Armours in Western Europe, Mozambique and Atlantic Accelerator. Whilst ammo boxes do not contain ammo for the Mjolnir by default it is possible to restock their ammo if you also carry a CQC11.

Notable Chapters

Chapter 8 - Play through the first half of the chapter and then take the Minigiun from the Reactive Armour. There are roughly 25 kills available between obtaining the weapon and the end of the level (assuming civilian kills don't count). It's worth considering the campaign for these kills as the Minigun has infinite ammo when found in the campaign.

Chapter 10 - Play through until you defeat the Reactive Armour and collect the Swarm. Proceed into the next area and start taking out the UAVs. Whilst the UAV kills don't count, once you've destroyed enough four enemies will spawn on the catwalk. After finishing these off proceed to the next checkpoint and then exit back to the main menu. Whilst this may be slower than co-op the fact that the Swarm only spawns on two maps and also requires you to be playing on at least Hard difficulty makes it worth considering.

Chapter 14 - Play through until you have passed through the first exterior section of the chapter and re-entered the tunnels and the first enemy you encounter will be carrying a Thermite. From this point to detonating the gas tank in the next external area there will be roughly 20 enemies. Once you are outside again there will be two enemies with Riot Shields and one carrying a LAWS-92. Switching the Thermite for the LAWS-92 allows roughly 8 kills before reaching the end of the level.

Chapter 17 - At the start of the chapter unlock the Beast of Burden Chip Upgrade allowing you to carry additional Grenades. When you exit the lift there will be Grenades available to pick up at the bottom of the stairs (activate DART if you're having trouble finding them). Equip these and then throw one at the group at the top of the stairs for three or four kills. Throw a second at the group exiting the VTOL for another 3 kills. Clear out the next few waves of enemies with your preferred gun and the equip your grenades again ready for the lift opening for another two kills (the Electric Armour here will also drop a Coil). Proceed into the next room and shoot the three enemies waiting for you, pick up additional Grenades if required and then ready yourself for waves of enemies to spawn from the lifts. This should provide another 12 kills. Then just enter the security room for a checkpoint and exit back to the main menu.

EDIT: Credit to Netrodude for the information on ammo for the Mjolnir.