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