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