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