Here is the full list of all 32 Just Sing trophies - there are 18 bronze, 8 silver, 5 gold and 1 platinum.
Sing 30 songs in Party Mode
Sing a song in Party mode with 2 or more performers
Upload 20 performances
Get 5 stars on 20 different songs with one performer
Accumulate 100 Stars in the Star Road
Sing 15 different songs
Get 5 stars on 10 different songs with one performer
Upload 10 performances
Get 5 stars on 5 different songs with one performer
Accumulate 20 Stars in the Star Road
Upload 5 performances
Upload 5 performances using 5 different themes directly from the Results menu
Get 5 stars on a song with one performer for the first time
Get 20 Perfect grades in a song
Get 10 consecutive Good or Perfect grades in a song
Upload your first performance
Select a theme and sing a song in Party mode
Sing a song in Party mode
Obtain all other Trophies
Get 5 stars on 40 different songs with one performer
Accumulate 250 Stars in the Star Road
Accumulate 500 Stars in the Star Road
Sing 50 songs in Party Mode
Sing 100 songs in Party Mode
Sing 30 different songs
Sing 45 different songs
Get all bonuses on Star Road
Play Battle mode for the first time
Play Battle mode 5 times
Play Battle mode 15 times
Play Battle mode 30 times
Sing a song with vocal track volume set to 0