Here is the full list of all 11 Lumines Supernova trophies - there are 6 bronze, 4 silver and 1 gold.
Unlock all skins.
Clear Puzzle Mode Hard.
Clear Mission Mode Hard.
Clear all stages in Dig Down Mode.
Unlock 10 skins in Challenge Mode "Advance".
Unlock 10 skins in Challenge Mode "Basic".
Clear Mission Mode Easy.
Clear Puzzle Mode Easy.
Unlock 3 skins in Challenge Mode "Basic".
Score 210 points in Time Attack Mode 180sec.
Score 50 points in Time Attack Mode 60sec.