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