Here is the full list of all 12 The Last Bounty Hunter trophies - there are 8 bronze, 3 silver and 1 gold.
Kill or capture Nasty Dan
Kill or capture El Loco
Kill or capture Handsome Harry
Kill or capture Cactus Kid
Kill all the bounties in one game
Capture all the bounties in one game
Win a showdown
Shoot six enemies in a row without missing or reloading
Shoot twelve enemies in a row without missing or reloading
Finish the game ( single player )
Complete the game in multiplayer mode
Complete a play through without killing any innocents