Here is the full list of all 31 Batman: Arkham Origins Blackgate trophies - there are 17 bronze, 7 silver, 6 gold and 1 platinum.
Unlock All Other Trophies
Find all detective cases and have all pickups and upgrades
Obtain all Batsuits attainable through gameplay
Defuse all Joker presents
Get a 100 hit combo
Get a 50 hit combo
Disarm all Black Mask junction boxes
Defeat Grundy using the Shock Batarang and water
Defeat Catwoman
Rescue all Penguin hostages
Unlock the Zombie Suit
Complete all detective cases
Find and destroy all of Black Mask's masks
Die from inhaling gas
Find all armor upgrades
Defeat Penguin
Find all gauntlet upgrades
Find and destroy all Penguin bird cages
Defeat Bronze Tiger
Defeat Black Mask
Find all RUSH upgrades
Defeat Joker
Beatdown 10 thugs
Find and destroy all Joker teeth
Get a 25 hit combo
Complete your first detective case
Defeat Deadshot
Perform 20 stealth takedowns
Defeat Solomon Grundy
Catch Catwoman in Gotham City
Get a 12 hit combo