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