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