Here is the full list of all 20 Huntdown trophies - there are 3 bronze, 8 silver, 8 gold and 1 platinum.
Trash a guitar on Sid Handsome
Kill 10 enemies with a Baseball Bat on one level
Press the retry button after completing a level
Complete a level without picking up any weapons
Watch all of Wolfmother's briefs without pressing skip
Make Suki the Sniper kill herself with her own missile
Restart more than 5 times during a fight with a bounty
Kill a bounty while having one health point left
Get hit by Nadja Drago's hockey stick and land in the goal
Kill a dog by making it fetch a grenade
Complete all Trophies in Huntdown
Get 100% completion in Normal Mode
Get 100% completion in Hard Mode
Get 100% completion in Badass Mode
Defeat the Shogun
Find at least 5 secret locations
Destroy 5 cars at the Overseer's Fume Pit without dying
Kick and shoot 10 enemies with a Shotgun before they hit the ground on one level
Get kicked out by Tony 5 times at the same checkpoint
Kill 10 enemies at close range with a Sawed-off on one level