Here is the full list of all 30 Batman: Arkham Origins Blackgate - there are Deluxe Edition achievements.
Defeat Catwoman
Defuse all Joker presents
Complete all detective cases
Unlock the Zombie Suit
Find all gauntlet upgrades
Find and destroy all Joker teeth
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
Defeat Penguin
Get a 50 hit combo
Beatdown 10 thugs
Defeat Deadshot
Die from inhaling gas
Defeat Solomon Grundy
Perform 20 stealth takedowns
Complete your first detective case
Get a 25 hit combo
Defeat Bronze Tiger
Catch Catwoman in Gotham City
Get a 12 hit combo
Find all detective cases and have all pickups and upgrades
Defeat Grundy using the Shock Batarang and water
Rescue all Penguin hostages
Disarm all Black Mask junction boxes
Get a 100 hit combo
Obtain all Batsuits attainable through gameplay