You must use each of the following melee weapons at least once to earn the trophy, getting a kill is not necessary for the trophy
Knife
Baseball Bat
Lead Pipe
Golf Club
Crowbar
Pool Cue
Pool Cue (Broken)
Frying Pan (Only found in chapter five on the second floor)
Pot (Chapter 2 and Chapter 4)
Katana
Sledgehammer
Machete
Baton (Only available in chapter 13)
Trophy (Only available during the final chapter)
Fireaxe
Drill (Only available while the "Carl" mask is equipped)
Briefcase (Only available during the Prelude)
The ninja star, beer can, dart, hammer, brick, scissors, glass bottle, and throwing knife are all thrown weapons and as such are not necessary to get this trophy.