You need to hit an enemy with every melee weapon in the game, as well as using every firearm as a melee weapon and using the taser. I would suggest writing down/printing off a list, and every time you use a weapon, cross it off.
The list of melee weapons is:
Rebar Conrete, Conduit, Sledgehammer, 2x4 Nails, 2x4 Bolts, Fire Axe, Large Pipe, Small Pipe, Rebar Bent, Shovel, Rebar, Crowbar, Mannequin Arm, Sign, Steam Pipe, Clothes Rack, Locker Door, Meat Cleaver, Paper Cutter, Gas Pipe, Desk Drawer, 2x4 Burnt, 2x4 Fire, Desktop, Stick, Large Plank, Fireplace Poker, .45 Cal, Revolver, Shotgun (pump), Shotgun (sawed-off), Sub-Machine Gun, Rifle, Taser
This achievement will only unlock at the end of a chapter, so if you have used all weapons and don't get it right away, make sure you finish the chapter to receive it.