Here is the full list of all 37 LEGO Harry Potter: Years 1-4 trophies - there are 18 bronze, 14 silver, 4 gold and 1 platinum.
Collect all the bronze, silver and gold trophies
Defeat 10 enemies with a Muggle character
Defeat Harry (as Voldemort), in the Graveyard
Defeat Quirrell in the Quirrell boss fight, using Voldemort
Destroy 50 Devil's Snare plants
Complete the game to 100%
Buy every version of Voldemort (Quirrell/Tom Riddle/Voldemort)
Collect all of the Gold Bricks
Rescue all students in peril
Collect all of the house crests in Year 4
Unlock all Animagi
Collect all of the house crests in Year 3
Collect all of the house crests in Year 2
Scare 20 students using a ghost character
Defeat 20 enemies with Fang
Defeat 20 spiders with Ron
Buy the entire Weasley family
Complete all the LEGO Builder tutorial levels.
Collect all of the house crests in Year 1
Collect all of the Red Bricks
Defeat the mountain troll, using Quirrell
Complete the Quidditch level within five minutes
Buy the entire Gryffindor Quidditch team from Book One
Hide in a barrel as Snape
Get True Wizard in every level
Complete the Story Levels in all four years
Complete Year Four Story Levels
Complete All Story Lessons
Use the Time-Turner
Turn the sound down to 0 and music off in the options menu whilst in the library
Complete Year Three Story Levels
Complete Year Two Story Levels
Collect 500 ghost studs
Freeze 20 characters using Glacius
Knock over ten characters using a ride-able object
Complete Year One Story Levels
Collect 10 million studs in one level