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