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