Here is the full list of all 64 Batman: Arkham City - there are Game of the Year Edition achievements.
Reveal the mystery watcher
Reunite the separated couple
Retrieve your stolen goods
Complete New Game Plus
Don't look down
Rescue the fourth hostage from Riddler
Destroy it all
Steal the score of a lifetime
Fight for survival
Stop the contract operative
A deadly game of hide and seek
Rescue the third hostage from Riddler
Rescue the second hostage from Riddler
We are legion
Uncover the secret of Arkham City
Collect all of Batman's gadgets and upgrades
Stop the unstoppable
A moment of remembrance
Last man standing
Solve the first riddle
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?
Stop all assaults in Arkham City
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
Use 5 different Quickfire gadgets in one fight as Robin in Harley Quinn's Revenge
Use 5 different Quickfire gadgets in one fight (any play mode)
Shield Bash 5 different thugs
Zip Kick 5 different thugs
Clear the airwaves
Track down the serial killer
Stop the phone booth killer
Time is running out
Complete all augmented reality training exercises
Rescue the first hostage from Riddler
Become the Bat
All the world is a stage
Rescue the fifth hostage from Riddler
Rescue all the hostages from Riddler
Obtain 24 medals on the original Arkham City maps (as Batman)
Obtain 48 medals on the original Arkham City maps (as Batman)
Obtain all 72 medals on the original Arkham City maps (as Batman)
Obtain 36 medals on the original Arkham City campaigns (as Batman)
Obtain 72 medals on the original Arkham City campaigns (as Batman)
Obtain all 108 medals on the original Arkham City campaigns (as Batman)
Complete one combat challenge without taking damage (any character)
Have 12 murderous dates with Calendar Man
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)
Complete all 40 of the Catwoman Riddler grid items
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)
Snap Flash an unarmed thug, an armed thug, an environmental object and a Titan
Destroy all Harley Balloons