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