Complete the following tasks to unlock Vita trophy rewards.

Trophy	How to unlock
2112 (Bronze)	Find all RUSH upgrades.
Armored Edition (Bronze)	Find all armor upgrades.
Bad Case of the Mondays (Gold)	Defeat Grundy using the Shock Batarang and water.
Bird on a Wire (Silver)	Find and destroy all Penguin bird cages.
Born on a Monday (Bronze)	Defeat Solomon Grundy.
Breathless (Bronze)	Die from inhaling gas.
CSI: Blackgate (Bronze)	Complete your first detective case.
Cage Match (Bronze)	Defeat Bronze Tiger.
Cat Scratch Fever (Gold)	Defeat Catwoman.
Circuit Breaker (Silver)	Disarm all Black Mask junction boxes.
Cobblepot's Plot Was All For Naught (Bronze)	Defeat Penguin.
Domestic Disturbance (Bronze)	Catch Catwoman in Gotham City.
Face Off (Bronze)	Defeat Black Mask.
Flew the Coop (Silver)	Rescue all Penguin hostages.
Fresh Beats (Bronze)	Beatdown 10 thugs.
Grave Digger (Gold)	Unlock the Zombie Suit.
He's Sleeping (Bronze)	Perform 20 stealth takedowns.
In the Flow (Bronze)	Get a 25 hit combo.
LEAGUE OF SHADOWS (Silver)	Get a 100 hit combo.
Last Laugh (Bronze)	Defeat Joker.
Now You're Getting It (Bronze)	Get a 12 hit combo.
Oral Hygiene (Silver)	Find and destroy all Joker teeth.
Party Pooper (Silver)	Defuse all Joker presents.
Talk to the Hand (Bronze)	Find all gauntlet upgrades.
The Collector (Gold)	Find every pickup and detective case.
The Dark Knight (Platinum)	Unlock All Other Trophies.
The Man Who Sometimes Misses (Bronze)	Defeat Deadshot.
Unmasked (Bronze)	Find and destroy all of Black Mask's masks.
Unnecessary Roughness (Silver)	Get a 50 hit combo.
World's Greatest Detective (Gold)	Complete all detective cases.
World's Snazziest Dresser (Gold)	Obtain all Batsuits attainable through gameplay.