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