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