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