Here is the full list of all 42 Tomb Raider: Legend trophies - there are 24 bronze, 14 silver, 3 gold and 1 platinum.
Earn all the trophies in Tomb Raider: Legend
Survive against Rutland for more than 5 minutes
Blow up 2 mercenaries with 1 propane tank while riding the motorcycle
Collect all gold rewards
Unlock all the outfits
Collect all bronze rewards
Collect all silver rewards
Complete the Bolivian temple without dying
Kill an enemy with a TV monitor
Kick the soccer ball against the door of the church in Peru
Kill 2 enemies during the same Aerial Attack
Complete all levels while in Time Trial mode
Complete the sixth level while in Time Trial mode
Complete the fourth level while in Time Trial mode
Complete the fifth level while in Time Trial mode
Complete the seventh level while in Time Trial mode
Complete the second level while in Time Trial mode
Complete the first level while in Time Trial mode
Complete the third level while in Time Trial mode
Complete Level 3 without using the dual pistols
Complete the game on Tomb Raider difficulty
Complete the game on Explorer or Adventurer difficulty
Complete the level "Nepal – The Ghalali Key"
Collect 60 common bronze rewards
Collect 30 precious silver rewards
Complete the level "England – King Arthur's Tomb?"
Collect 5 rare gold rewards
Listen to the tale of King Arthur
Complete the level "Kazakhstan – Project Carbonek"
Kill 2 enemies by detonating a fuel tank
Collect 35 common bronze rewards
Complete the level "Ghana – Pursuing James Rutland"
Shoot out the 4 flood lights in the water wheel room in level 4
Complete the level "Tokyo – Meeting with Takamoto"
Complete the level "Peru – Return to Paraíso"
Collect 1 gold reward
Destroy 10 boxes while on the motorcycle in Peru
Kill an enemy by detonating a fuel tank
Kill an enemy with an Aerial Attack
Complete the level "Bolivia – Tiwanaku"
Collect 5 common bronze rewards
Collect a reward