Here is the full list of all 9 SingStar SuomiHelmet trophies - there are 5 bronze, 2 silver and 2 gold.
Sing your first song
Sing 20 songs
Sing 50 songs
Sing 100 songs
Gain the number 1 position in 10 different score charts
Perform vibrato for 100 seconds
Accumulate 3000 seconds of perfect pitch
Perform with a friend 20 times
Play on SingStar's original launch date