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