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