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