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