Here is the full list of all 33 Sophstar trophies - there are 23 bronze, 3 silver, 6 gold and 1 platinum.
Earn all trophies
Start a game on any mode or difficulty for the first time.
Face the true last boss.
Score 500000 points in arcade mode (Original).
Score 2000000 points in arcade mode (Original).
Score 5000000 points in arcade mode (Original).
Make a 100x chain in Arcade mode (Advanced).
Destroy 30 enemies in a row at 9x chain in arcade mode (Original).
Finish a level without using a teleport.
Play in TATE mode.
Finish the arcade mode using Dumont.
Finish the arcade mode using Leo.
Finish the arcade mode using Nina.
Finish the arcade mode using Rigby.
Finish the arcade mode using Arobe-D.
Finish the arcade mode using Katha.
Finish the arcade mode using Hirane.
Finish the arcade mode using Reyka.
Finish the arcade mode using Z2.
Grab some boss pieces that were left behind.
Select Reyka for the first time.
Select Hirane for the first time.
Select Katha for the first time.
Select Nina for the first time.
Select Dumont for the first time.
Select Z2 for the first time.
Select Arobe-D for the first time.
Select Rigby for the first time.
Select Leo for the first time.
Finish score attack mode.
Have at least 2 minutes remaining on Timed Challenge.
Get 3 secret bonus.
Played an endless mode up until the end.