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