Here is the full list of all 32 SingStar (EU) trophies - there are 18 bronze, 8 silver, 5 gold and 1 platinum.
Perform 100 songs
Complete 5 rap performances
Complete 5 performances of a duet song with another player
Rate 10 pieces of media
View 50 pieces of media
Perform 15 songs in one game session
Get the highest ranking on 10 lines in a row
Complete 500 Golden Notes
Perform with a friend 30 times
Play 5 random songs selected by the Shuffle button
Perform 40 songs
Accumulate 3000 seconds of perfect pitch
Play on SingStar's original launch date
Perform a duet song on St. Valentine's Day
Get the lowest score rank on any song
Gain the number 1 position in 10 different score charts
Fill every Golden Note in a normal length performance
Accumulate 500 seconds of perfect pitch
Play on Christmas Day
Perform vibrato for the first time
Collect every SingStar™ trophy
Perform 400 songs
Perform with a friend 90 times
Perform with a friend 300 times
Earn the "SingStar" score ranking in 10 normal length performances
Earn the "SingStar" score ranking in 20 normal length performances
Perform vibrato for a total of 300 seconds
Get the highest ranking on every line in a Normal length performance
Accumulate 10000 seconds of perfect pitch
Sing in harmony with a friend during a duet song
Upload a piece of media
Save 20 pieces of media