Here is the full list of all 25 Graceful Explosion Machine trophies - there are 6 bronze, 12 silver, 6 gold and 1 platinum.
Complete every WARP+ level
Complete the game
S Rank an entire planet
Complete Scarlet Epsilon
Get a 48x combo
Die with less than 10% left on the Enemies Left meter
Destroy 30 bullets using the Energy Sword in a single level
Finish a level without flipping (excluding tutorial levels)
Get 20 hits with a single Sniper Beam blast
First S+ Rank
Replay a level and get an improved rank
Finish a level without taking damage (excluding tutorial levels)
Complete Quartz Catacombia
Complete Magentos Prime
First S Rank
Get a 32x combo
Complete a phase without dropping the combo multiplier
First A Rank
Get a 16x combo
Perform a 4x (or greater) combo that uses every weapon
Fire 100+ Missiles in a level
All weapons active
Complete Tutorial 1
Graceful-est Explosion Machine
S Rank all planets