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