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