Here is the full list of all 39 LEGO Indiana Jones 2: The Adventure Continues trophies - there are 14 bronze, 22 silver, 2 gold and 1 platinum.
All trophies unlocked
Complete all Story Levels in Quick Play modes.
Complete Hangar 51 in under 5 minutes.
Complete the game to 100%
Use Scholar access 10 times.
Defeat 50 Russians with Mutt.
Edit a Bonus level in the Builder.
Destroy Indy with Spalko.
Complete all Bonus Levels in Crusade Hub.
Find all the Artifacts in the game.
Complete all Treasure Mode Levels in Crusade Hub.
Unlock all of the enemies in the game.
Complete all plane races.
Unlock all of the vehicles in the game.
Unlock the Grail Knight.
Complete all Bonus Levels in Temple of Doom Hub.
Complete all Treasure Mode Levels in Temple of Doom Hub.
Complete all Bonus Levels in Raiders Hub.
Complete all Treasure Mode Levels in Raiders Hub.
Complete all Bonus Levels in Skull 3 Hub.
Unlock the Interdimensional Being.
Complete all Treasure Mode Levels in Skull 3 Hub.
Complete all Story Mode Levels in Crusade Hub.
Complete all Story Mode Levels in Temple of Doom Hub.
Complete all Story Mode Levels in Raiders Hub.
Destroy 100 enemy vehicles.
Complete all Bonus Levels in Skull 2 Hub.
Complete all Treasure Mode Levels in Skull 2 Hub.
Complete all Story Mode Levels in Skull 3 Hub.
Fire a Bazooka 100 times.
Complete all Story Mode Levels in Skull 2 Hub.
Complete a "Build Your Own Adventure".
Create a validated Builder level.
Complete the Builder Tutorial levels.
Destroy Indy 3 times with Mac.
Complete all Bonus Levels in Skull 1 Hub.
Complete all Treasure Mode Levels in Skull 1 Hub.
Create a customised character.
Complete all Story Mode Levels in Skull 1 Hub.