Here is the full list of all 39 Jak and Daxter: The Precursor Legacy trophies - there are 22 bronze, 12 silver, 4 gold and 1 platinum.
The Final Battle Against Gol and Maia
Free the Green Sage
Free the Blue Sage
Free the Red Sage
Free the Yellow Sage
Reach the End of the Lava Tube
Survive the Lurker Infested Cave
Stop the 3 Lurker Glacier Troops
Reach the End of the Mountain Pass
Defeat Klaww
Collect 50 Power Cells
Beat the Record Time on the Gorge
Cure Dark Eco Infected Plants
Navigate the Purple Precursor Rings
Catch the Flying Lurkers
Collect 1000 Precursor Orbs
Protect Farthy's Snacks
Collect 49 Scout Flies
Defeat the Lurker Ambush
Reach the End of Fire Canyon
Collect 25 Power Cells
Collect 28 Scout Flies
Destroy the Balloon Lurkers
Defeat Lurker Ambush in Arena
Get the Power Cell from the Pelican
Push the Flut Flut Egg Off the Cliff
Herd the Yakows in to their Pen
Catch 200 Pounds of Fish
Defeat the Dark Eco Plant
Collect 100 Precursor Orbs
Open the Precursor Door
You have mastered the game and collected all there is to collect!
Connect the Eco Beams
Navigate the Blue Precursor Rings
Break all Four Tethers to the Zeppelin
Destroy the Dark Eco Crystals
Collect 101 Power Cells
Collect 112 Scout Flies
Collect 2000 Precursor Orbs