Here is the full list of all 30 Batman: Arkham Origins Blackgate - there are Deluxe Edition achievements.
Defeat Catwoman
Rescue all Penguin hostages
Find all gauntlet upgrades
Defeat Joker
Defeat Penguin
Defeat Black Mask
Beatdown 10 thugs
Defeat Solomon Grundy
Defeat Grundy using the Shock Batarang and water
Perform 20 stealth takedowns
Complete your first detective case
Find and destroy all Joker teeth
Die from inhaling gas
Defeat Bronze Tiger
Get a 25 hit combo
Catch Catwoman in Gotham City
Get a 12 hit combo
Find all detective cases and have all pickups and upgrades
Defeat Deadshot
Defuse all Joker presents
Disarm all Black Mask junction boxes
Get a 50 hit combo
Get a 100 hit combo
Unlock the Zombie Suit
Complete all detective cases
Find and destroy all Penguin bird cages
Find and destroy all of Black Mask's masks
Obtain all Batsuits attainable through gameplay
Find all armor upgrades
Find all RUSH upgrades