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