Here is the full list of all 47 Batman: Arkham Asylum GOTY achievements worth 1,000 gamerscore.
Ride Titan henchman and knock down 10 thugs (any play mode)
Solve 55% of Riddler challenges
Venture into Killer Croc's lair and come out alive
Conquer the effects of the Scarecrow's fear gas
Defeat two Titan Henchmen at once
String up one henchman and drop him to surprise a second (any play mode)
Solve 40% of Riddler challenges
Catch a Batarang (any play mode)
Capture and lock up Harley Quinn
Save Dr. Young from being killed by Victor Zsasz
Face your biggest fears and keep your sanity
Solve 25% of Riddler challenges
Complete a combo of 20 moves (any play mode)
Gain access to Arkham Mansion after it is locked down by the Joker
Glide continuously for over 100m
Defeat Bane
Complete a combo of 10 moves (any play mode)
Solve 10% of Riddler challenges
Survive the nightmare of the Scarecrow's fear gas
Save all the doctors in Medical
Solve 5% of Riddler challenges
Escape from Intensive Treatment to the island surface
Survive the onslaught from the deformed Joker henchman
Rescue the guards and henchman from the Joker toxin in Decontamination
Take down Zsasz in the Patient Pacification Chamber
Complete a combo of 5 moves (any play mode)
Defeat the giant Titan Ivy plant
Complete story mode on Easy difficulty
Complete story mode on Normal difficulty
Complete story mode on Hard difficulty
Time to break up this party
Complete a combo of 40 moves (any play mode)
Take on a beast in hand to hand combat
Perform a perfect combo including all of Batman's combat moves (any play mode)
Achieve 8 medals on combat challenges
Achieve 16 medals on combat challenges
Achieve 24 medals on combat challenges
Achieve 8 medals on predator challenges
Achieve 16 medals on predator challenges
Achieve 24 medals on predator challenges
Complete one predator challenge by using only Silent Takedowns and without being detected
Complete one combat challenge without taking damage
Solve every riddle on the island
Solve 70% of Riddler challenges
Solve 85% of Riddler challenges
Solve Arkham's biggest mystery
100% Complete