There are 42 Trophies that can be collected.

Bronze

Bilateral Disarmament
Turn off both dart shooters in the Mountain Entrance hall in Peru

Getting the Goods
Find an artifact or relic

Hot Shot
Kill 3 enemies with an Adrenaline Dodge and head Shot attack.

In High Gear
Complete the Peru gear puzzle without dying.

Peruvian Raider
Complete the Peru chapter.

Good Show in Peru
Complete all the Peru Super Actions without dying.

Peruvian 'fact Finder
Collect all the artifacts in Peru.

Weapon Master I
Collect the Shotgun.

Queen of the Jungle
Kill a lion with an Adrenaline Head Shot.

Greek to Me
Complete the Greece chapter.

Weapon Master II
Collect the Dual .50 Caliber Pistols.

Greek 'fact Finder
Collect all the artifacts in Greece.

Good show in Greece
Complete all the Greece Super Actions without dying.

Like a Rolling Stone
Kill 6 rats with a boulder in Egypt.

Sign Seals Delivered
Collect the seals of Anubis, Horus, Isis and Osiris.

Good Show in Egypt
Complete all the Egypt Super Actions without dying.

Raid Like an Egyptian
Complete the Egypt chapter.

Lost Island Tomb Raider
Complete the Lost Island chapter.

Weapon Master III
Collect the Dual Mini SMGs

Slayer I
Defeat the boss in Peru without dying.

Egyptian 'fact Finder
Collect all the artifacts in Egypt.

Lost Island 'fact Finder
Collect all the artifacts on the Lost Island.

Silver

Lightning Never Strikes Twice
Complete the Hephaestus room in Greece without being struck by lightning.

Central Shaft Survivor
Complete the central shaft in the Lost Island without dying.

Slayer II
Defeat the boss in Greece without dying.

Slayer III
Defeat the first boss on the Lost Island without dying.

Slayer IV
Defeat the final boss on the Lost Island without dying.

Homebody
Complete all of the challenges in Croft Manor.

Peruvian Reliquarian
Collect all the relics in Peru.

Greek Reiquarian
Collect all the relics in Greece.

Egyptian Reliquarian
Collect all the relics in Egypt.

Lost Island Reliquarian
Collect all the relics in Lost Island.

Peruvian Speed Run
Complete all the Time Trials in Peru.

Greek Speed Run
Complete all the Time Trials in Greece.

Egyptian Speed Run
Complete all the Time Trials in Egypt.

Lost Island Speed Run
Complete all the Time Trials in Lost Island.

Home Run
Complete the Time Trial in Croft Manor.

Good Show on Lost Island
Complete all the Lost Island Super Actions without dying.

Sweet Victory
Complete the game.

Gold

Dressed to Kill
Unlock all the outfits.

Tough Enough
Complete the game on Hard difficulty.

Platinum

Master of Tomb Raider: Anniversary
Earn all the trophies in Tomb Raider: Anniversary.

http://www.ps3trophies.org/game/tomb-raider-anniversary/trophies/