Here is the full list of all 37 LEGO Harry Potter: Years 1-4 trophies - there are 20 bronze, 12 silver, 4 gold and 1 platinum.
Collect all of the Red Bricks
Collect 10 million studs in one level
Turn the sound and music down to 0 in the options menu whilst in the library
Defeat 20 spiders with Ron
Defeat 20 enemies with Fang
Complete the Quidditch level within five minutes
Complete the Story Levels in all four years
Complete Year Four Story Levels
Complete All Story Lessons
Use the Time-Turner
Complete Year Three Story Levels
Collect 500 ghost studs
Complete Year Two Story Levels
Knock over ten characters using a ride-able object
Complete Year One Story Levels
Collect all the bronze, silver and gold trophies
Collect all of the house crests in Year 1
Collect all of the house crests in Year 2
Collect all of the house crests in Year 3
Collect all of the house crests in Year 4
Collect all of the Gold Bricks
Rescue all students in peril
Get True Wizard in every level
Complete the game to 100%
Buy every version of Voldemort (Quirrell/Tom Riddle/Voldemort)
Buy the entire Gryffindor Quidditch team from Book One
Complete all the LEGO Builder tutorial levels.
Buy the entire Weasley family
Defeat Quirrell in the Quirrell boss fight, using Voldemort
Freeze 20 characters using Glacius
Scare 20 students using a ghost character
Unlock all Animagi
Defeat the mountain troll, using Quirrell
Hide in a barrel as Snape
Defeat Harry (as Voldemort), in the Graveyard
Defeat 10 enemies with a Muggle character
Destroy 50 Devil's Snare plants