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