Here is the full list of all 11 Galak-Z: The Dimensional trophies - there are 7 bronze, 3 silver and 1 gold.
Unlock All Trophies
Complete Mech Tutorial
Defeat the Pirate King
Complete Intro Tutorial
Complete Season One
Complete Season Two
Complete Season Three
Complete Season Four
Defeat 100 Void Raiders
Defeat 100 Imperials
Defeat 100 Space Bugs