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
Unlock all Characters
Complete All Multi-Part Challenges
Rescue All Civilians and Master Builders
Complete All Timed Challenges
Collect All Minikits
Defeat 50 Enemies using Bad Cop
Have Batman, Superman, Wonder Woman and Green Lantern in the same party
Destroy all Lord Business statues
Complete a Skydive as Superman
Collect All Missing Pants
Collect All Red Bricks
Defeat Lord Business With Vitruvius In Your Party
Destroy every SSP Dropship in the game
Finish "The Cube Ship"
Finish "Attack on Bricksberg"
Complete a Build-It or Master Build as Emmet
Finish "Spaceship Escape"
Finish "TV Station"
Defeat one of each enemy type
Finish "The Kragle"
Finish "Business HQ"
Defeat 100 enemies using special moves
Finish "Submarine"
Finish "Cloud Under Attack"
Defeat 20 Enemies using Batman's special moves
Déjà Vu for Gandalf
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