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