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