Here is the full list of all 30 Batman: Arkham Origins Blackgate Deluxe Edition achievements worth 400 gamerscore.
Obtain all batsuits attainable through gameplay
Find every pickup and detective case
Disarm all Black Mask junction boxes
Defeat Grundy using the Shock Batarang and water
Rescue all Penguin hostages
Defeat Catwoman
Defuse all Joker presents
Unlock the Zombie Suit
Complete all detective cases
Find all gauntlet upgrades
Find and destroy all Joker teeth
Defeat Joker
Find and destroy all of Black Mask's masks
Find all armor upgrades
Find all RUSH upgrades
Defeat Black Mask
Find and destroy all Penguin bird cages
Defeat Penguin
Get a 100 hit combo
Get a 50 hit combo
Perform 20 stealth takedowns
Defeat Deadshot
Die from inhaling gas
Defeat Solomon Grundy
Complete your first detective case
Defeat Bronze Tiger
Catch Catwoman in Gotham City
Beatdown 10 thugs
Get a 25 hit combo
Get a 12 hit combo