Here is the full list of all 12 Puzzle Quest Galactrix trophies - there are 8 bronze, 3 silver and 1 gold.
You have reached Level 50.
You have defeated the Gamma Sphere.
You have successfully mined 10 asteroids.
You have defeated the Luminary Archive.
You have unlocked a rumor.
You have won 50 ranked PlayStation®Network matches.
You have won 5 ranked PlayStation®Network matches.
You have captured a Soulless and discovered their true nature.
You have unlocked all Psi Powers.
You have completed the Haggling minigame with 6 Gems or less on the board.
You have hacked 30 LeapGates.
You have hacked a LeapGate.