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