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