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
Destroy the Dark Eco Crystals
Beat the Record Time on the Gorge
Navigate the Purple Precursor Rings
Cure Dark Eco Infected Plants
Collect 1000 Precursor Orbs
Reach the End of the Mountain Pass
Collect 50 Power Cells
Defeat Klaww
Collect 49 Scout Flies
Protect Farthy's Snacks
Break all Four Tethers to the Zeppelin
Defeat the Lurker Ambush
Reach the End of Fire Canyon
Collect 25 Power Cells
Destroy the Balloon Lurkers
Defeat Lurker Ambush in Arena
Collect 28 Scout Flies
Connect the Eco Beams
Defeat the Dark Eco Plant
Catch 200 Pounds of Fish
Push the Flut Flut Egg Off the Cliff
Collect 100 Precursor Orbs
Herd the Yakows in to their Pen
Open the Precursor Door
You have mastered the game and collected all there is to collect!
Get the Power Cell from the Pelican
Catch the Flying Lurkers
Navigate the Blue Precursor Rings
Stop the 3 Lurker Glacier Troops
Collect 101 Power Cells
Collect 112 Scout Flies
Collect 2000 Precursor Orbs