Here is the full list of all 13 Symphony of the Machine trophies - there are 9 bronze, 3 silver and 1 gold.
Call a Storm
Bloom the Anther Plant
Going down in a bloom of glory
Spawn a Tornado
Split the beam into four
Reflect the laser 4 times
Create a double rainbow
Overload the tower
Put 5 objects into the robot's carrying space
Use all the mirrors and splitters to turn on one glyph
You were mean to the robot with every tool. Poor thing.
Get all the weather types
Just like home