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)
Have 12 murderous dates with Calendar Man
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)
Complete every challenge in Arkham City - Main Story, Side Missions, Upgrades, Collectables, New Game Plus and Riddlers Revenge (as Batman)
Obtain all 72 medals on the original Arkham City maps (as Catwoman)
Destroy all Harley Balloons
Snap Flash an unarmed thug, an armed thug, an environmental object and a Titan
Use 5 different Quickfire gadgets in one fight as Robin in Harley Quinn's Revenge
Shield Bash 5 different thugs
A moment of remembrance
Complete all 40 of the Catwoman Riddler grid items
Rescue all the hostages from Riddler
Obtain all 108 medals on the original Arkham City campaigns (as Batman)
Track down the serial killer
Rescue the fifth hostage from Riddler
Retrieve your stolen goods
Complete all augmented reality training exercises
Stop all assaults in Arkham City
Use 5 different Quickfire gadgets in one fight (any play mode)
Stop the contract operative
Stop the phone booth killer
Obtain all 72 medals on the original Arkham City maps (as Batman)
Obtain 72 medals on the original Arkham City campaigns (as Batman)
Reunite the separated couple
Reveal the mystery watcher
Complete New Game Plus
Destroy it all
Rescue the fourth hostage from Riddler
Obtain 48 medals on the original Arkham City maps (as Batman)
Rescue the third hostage from Riddler
Collect all of Batman's gadgets and upgrades
Time is running out
Obtain 36 medals on the original Arkham City campaigns (as Batman)
Zip Kick 5 different thugs
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
Rescue the second hostage from Riddler
Rescue the first hostage from Riddler
Solve the first riddle
All the world is a stage
Don't look down
Obtain 24 medals on the original Arkham City maps (as Batman)
Steal the score of a lifetime
Fight for survival
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
Complete one combat challenge without taking damage (any character)
Drop in on an old friend
Hammer the point home
There is only one way in
Save the medical volunteers
Save the damsel, but is she in distress?
Become the Bat