Below is a list of all weapons need along with the player(s) that are needed to use each weapon. To check and see how many kills you have with each weapon, go to Records from the Main Menu, then Weapons and check for Enemies Defeated. Make sure you look at enemies defeated and not Times Used which is the number that is next to the gun. Simply load the chapter you need or Mercenaries mode with the right person get your required kills then back out. Play until you get 10 kills per weapon and the achievement should pop right away.
Here is all weapons that are required for the achievement if it's not listed then you do not need that weapon.
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Nine-Oh-Nine 909 - Jake and Chris
Picador - Helena
Wing Shooter - Leon
Shotgun - Leon,Helena,Jake,Sherry
Assault Shotgun - Chris and Piers chapter 2 and Ada
Hydra - Helena
Lightning Hawk - Leon and Helena
Elephant Killer - Jake and Sherry
Sniper Rifle - Jake,Sherry,Ada
Semi-Automatic SR - Leon,Helena,Chris,Piers
Anti-Materiel Rifle - Piers
Ammo Box 50 - Ada
Triple Shot - Sherry
MP-AF (Machine Pistol - Accurate Fire) - Piers
Assault Rifle for Special Tactics - Chris
Bear Commander - Jake and Sherry Chapter 3 and Ada
Assault Rifle RN - Leon and Helena Chapter 3
Grenade Launcher - Chris and Piers Chapter 3
Crossbow - Ada
Survival Knife - Leon only
Combat Knife - Chris only
Stun Rod - Sherry only
Video Credit goes to Gamer=Digital Concept