Here is the full list of all 35 The LEGO Movie Videogame trophies - there are 20 bronze, 9 silver, 5 gold and 1 platinum.
Collect All Trophies
Complete All Timed Challenges
Unlock all Characters
Collect All Minikits
Rescue All Civilians and Master Builders
Complete All Multi-Part Challenges
Collect All Red Bricks
Collect All Missing Pants
Destroy all Lord Business statues
Defeat 50 Enemies using Bad Cop
Have Batman, Superman, Wonder Woman and Green Lantern in the same party
Déjà Vu for Gandalf
Destroy every SSP Dropship in the game
Complete a Skydive as Superman
Defeat Lord Business With Vitruvius In Your Party
Defeat 20 Enemies using Batman's special moves
Finish "The Cube Ship"
Finish "Attack on Bricksberg"
Complete a Build-It or Master Build as Emmet
Defeat 100 enemies using special moves
Finish "Spaceship Escape"
Finish "TV Station"
Defeat one of each enemy type
Finish "The Kragle"
Finish "Business HQ"
Finish "Submarine"
Finish "Cloud Under Attack"
Finish "Cloud Cuckoo Land"
Finish "Flatbush Chase"
Finish "Flatbush Rooftops"
Finish "Flatbush Town"
Finish "Flatbush Gulch"
Finish "Police Station"
Finish "Prologue"
Complete an Instruction Build