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