Here is the full list of all 41 Jak II trophies - there are 26 bronze, 10 silver, 4 gold and 1 platinum.
Beat Krew in Weapons Lab
Defeat Baron in Mar's Tomb
Destroy Eggs at Drill Platform using the touchscreen
Defeat Baron at Palace
Get Seal Piece at Dig
Get Heart of Mar in Weapons Lab
Ride Elevator up to Palace
Blow up Strip Mine in Eco Wells
Win Class 3 Race at Stadium
Escort Men Through Sewers
Pass the Tests of Manhood
Use Items in No Man's Canyon
Collect Money for Krew
Destroy Metal Kor at Nest
Turn on 5 Power Switches
Find 3 Artifacts in Mountain Temple
Rescue Vin at Strip Mine
Find Pumping Station Patrol
Destroy Turrets in Sewers
Protect Sig at Pumping Station
Blow up Ammo at Fortress
Retrieve Banner from Dead Town
Protect Kor and Kid
For excellent and dedicated field work in the field of battle for completion.
Catch Scouts in Haven Forest
Destroy Equipment at Dig
Destroy Ship at Drill Platform
Destroy 5 Hellcat Cruisers
Rescue Friends at Fortress
Protect Hideout from Bomb Bots
Win Class 2 Race at Stadium
Destroy Drill Platform Tower
Win Class 1 Race in Stadium
Find Sig in Underport
Attack the Metal Head Nest
Collect 50 Metal Head Skull Gems
Collect 250 Metal Head Skull Gems
Collect 510 Metal Head Skull Gems
Collect 25 Precursor Orbs
Collect 125 Precursor Orbs
Collect 286 Precursor Orbs