Here is the full list of all 30 Batman: Arkham Origins Blackgate - there are Deluxe Edition achievements.
Defeat Catwoman
Rescue all Penguin hostages
Defuse all Joker presents
Disarm all Black Mask junction boxes
Find all detective cases and have all pickups and upgrades
Complete all detective cases
Unlock the Zombie Suit
Obtain all Batsuits attainable through gameplay
Find all gauntlet upgrades
Find all armor upgrades
Defeat Grundy using the Shock Batarang and water
Find and destroy all of Black Mask's masks
Get a 100 hit combo
Defeat Black Mask
Find and destroy all Penguin bird cages
Find all RUSH upgrades
Defeat Solomon Grundy
Defeat Joker
Beatdown 10 thugs
Defeat Penguin
Find and destroy all Joker teeth
Get a 50 hit combo
Complete your first detective case
Perform 20 stealth takedowns
Defeat Deadshot
Die from inhaling gas
Defeat Bronze Tiger
Catch Catwoman in Gotham City
Get a 25 hit combo
Get a 12 hit combo