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