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