Here is the full list of all 31 Batman: Arkham Origins Blackgate Deluxe Edition 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
Complete all detective cases
Disarm all Black Mask junction boxes
Defeat Catwoman
Rescue all Penguin hostages
Unlock the Zombie Suit
Defeat Penguin
Find all armor upgrades
Find all gauntlet upgrades
Defeat Joker
Find and destroy all of Black Mask's masks
Defeat Black Mask
Find all RUSH upgrades
Find and destroy all Penguin bird cages
Defeat Grundy using the Shock Batarang and water
Defeat Solomon Grundy
Perform 20 stealth takedowns
Find and destroy all Joker teeth
Get a 100 hit combo
Beatdown 10 thugs
Get a 50 hit combo
Defeat Deadshot
Die from inhaling gas
Complete your first detective case
Get a 25 hit combo
Defeat Bronze Tiger
Catch Catwoman in Gotham City
Get a 12 hit combo