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