Here is the full list of all 32 Tomb Raider: Anniversary achievements worth 1,000 gamerscore.
Completed all the Peru Time Trials.
Completed all Lost Island Time Trials.
Collected all the relics and artifacts in Lost Island.
Complete all the Greece Time Trials.
Completed all the Egypt Time Trials.
Completed the Croft Manor Time Trial.
Completed all the Lost Island Super Actions without fail (first try).
Completed Lost Island without dying.
Completed the game on Easy difficulty.
Completed the game on Medium difficulty (includes Easy Game achievement).
Completed the game on Hard difficulty (includes Easy and Medium Game achievements).
Defeated Natla without dying (Lost Island).
Defeated the Torso Boss without dying (Lost Island).
Completed the central shaft in the Lost Island without dying.
Completed all the Egypt Super Actions without fail (first try).
Completed Egypt without dying.
Collected all the artifacts and relics in Egypt.
Collected the Uzi weapon.
Collected the seals of Anubis, Horus, Isis, and Osiris without dying.
Completed all the Greece Super Actions without fail (first try).
Completed Greece without dying.
Defeated the Twin Centaur Bosses without dying (Greece).
Collected all the artifacts and relics in Greece.
Collected the Magnum weapon.
Completed the Hephaestus room in Greece without being struck by lightning.
Completed all the Peru Super Actions without fail (first try).
Completed Peru without dying.
Collected all the artifacts and relics in Peru.
Completed the Peru gear puzzle without dying.
Defeated the T-Rex without dying (Peru).
Collected the Shotgun weapon.
Completed all challenges in the Croft Manor.