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
Defuse all Joker presents
Rescue all Penguin hostages
Defeat Grundy using the Shock Batarang and water
Get a 100 hit combo
Defeat Catwoman
Disarm all Black Mask junction boxes
Unlock the Zombie Suit
Complete all detective cases
Die from inhaling gas
Find all armor upgrades
Defeat Black Mask
Find and destroy all of Black Mask's masks
Find and destroy all Penguin bird cages
Find all RUSH upgrades
Find all gauntlet upgrades
Find and destroy all Joker teeth
Defeat Penguin
Defeat Joker
Beatdown 10 thugs
Defeat Solomon Grundy
Perform 20 stealth takedowns
Get a 50 hit combo
Defeat Deadshot
Complete your first detective case
Defeat Bronze Tiger
Get a 25 hit combo
Get a 12 hit combo
Catch Catwoman in Gotham City