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