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
Complete all detective cases
Obtain all Batsuits attainable through gameplay
Rescue all Penguin hostages
Find all RUSH upgrades
Find all gauntlet upgrades
Find all armor upgrades
Find and destroy all of Black Mask's masks
Complete your first detective case
Unlock the Zombie Suit
Disarm all Black Mask junction boxes
Get a 100 hit combo
Defeat Catwoman
Find and destroy all Joker teeth
Defuse all Joker presents
Die from inhaling gas
Get a 50 hit combo
Find and destroy all Penguin bird cages
Defeat Joker
Defeat Black Mask
Defeat Penguin
Defeat Bronze Tiger
Perform 20 stealth takedowns
Beatdown 10 thugs
Defeat Solomon Grundy
Defeat Grundy using the Shock Batarang and water
Get a 25 hit combo
Defeat Deadshot
Catch Catwoman in Gotham City
Get a 12 hit combo