Here is the full list of all 64 Batman: Arkham City - there are Game of the Year Edition achievements.
Perform a perfect combo including all of Batman's combat moves (any play mode)
Have 12 murderous dates with Calendar Man
Snap Flash an unarmed thug, an armed thug, an environmental object and a Titan
Destroy all Harley Balloons
Obtain all 108 medals on the original Arkham City campaigns (as Batman)
Complete every challenge in Arkham City - Main Story, Side Missions, Upgrades, Collectables, New Game Plus and Riddlers Revenge (as Batman)
Obtain 72 medals on the original Arkham City campaigns (as Batman)
Obtain 36 medals on the original Arkham City campaigns (as Batman)
Obtain all 72 medals on the original Arkham City maps (as Batman)
Obtain 48 medals on the original Arkham City maps (as Batman)
The joke's on who?
Defuse all bombs in 3 minutes or less
Use 5 different Quickfire gadgets in one fight as Robin in Harley Quinn's Revenge
Shield Bash 5 different thugs
Clean up the Dry Docks
Zip Kick 5 different thugs
Find a way into the secret base
No crimefighter should be without this
Obtain 24 medals on the original Arkham City maps (as Batman)
Complete New Game Plus
A moment of remembrance
Complete all 40 of the Catwoman Riddler grid items
Track down the serial killer
Reveal the mystery watcher
Rescue all the hostages from Riddler
Stop all assaults in Arkham City
Retrieve your stolen goods
Stop the contract operative
Rescue the fifth hostage from Riddler
Collect all of Batman's gadgets and upgrades
Stop the phone booth killer
Rescue the fourth hostage from Riddler
Use 5 different Quickfire gadgets in one fight (any play mode)
Complete one combat challenge without taking damage (any character)
Reunite the separated couple
Destroy it all
All the world is a stage
Don't look down
Steal the score of a lifetime
Fight for survival
Rescue the third hostage from Riddler
A deadly game of hide and seek
Time is running out
We are legion
Uncover the secret of Arkham City
Stop the unstoppable
Last man standing
Rescue the second hostage from Riddler
Clear the airwaves
Rescue the first hostage from Riddler
Complete all augmented reality training exercises
Become the Bat
Save the damsel, but is she in distress?
Save the medical volunteers
There is only one way in
Hammer the point home
Solve the first riddle
Drop in on an old friend
Obtain all 72 medals on the original Arkham City maps (as Catwoman)
Obtain all 108 medals on the original Arkham City campaigns (as Catwoman)
Obtain 78 medals on the original Arkham City and Robin Bundle Pack maps (as Robin)
Obtain 114 medals on the original Arkham City and Robin Bundle Pack campaigns (as Robin)
Obtain 78 medals on the original Arkham City and Nightwing Bundle Pack maps (as Nightwing)
Obtain 114 medals on the original Arkham City and Nightwing Bundle Pack campaigns (as Nightwing)