Here is the full list of all 35 Ratchet & Clank trophies - there are 19 bronze, 10 silver, 5 gold and 1 platinum.
Attain 15 Skill Points to Unlock Sketchbook in Menu
Shoot a Scream through the sniper hole on Orxon
Kill all Anklebiters on Planet Hoven
Find and destroy all the crates in the ocean on Pokitaru
Defeat Blarg Station Alien Queen using only the wrench!
Do a "Twisty" McMarx" in the hoverboard race
Lure an enemy into a forcefield on Orxon
Obtain the Premium Nanotech upgrade
Obtain the Magneboots
Destroyed three flying transports on Aridia
Destroy a fighter or bomber on Novalis
Destroy Captain Qwark training robot on Kerwan
Blow Up 10 Vehicles on Eudora
On Gaspar, blow up all Blarg destroyers
Beat the hoverboard challenge in less than 1:35 on Rilgar
Obtain the Suck Cannon
Stand between Al's Roboshack Statue's legs on Kerwan
Obtain All Ratchet & Clank Trophies
Gather All 40 Golden Bolts throughout the game
Master all 30 skill points
Obtain all ten gold weapons
Defeat Chairman Drek
Obtain the R.Y.N.O.
Destroy all streetlights in Oltanis
Obtain all regular weapon gadgets
Upgrade to Ultra Nanotech
Collect 1,000,000 Bolts
Defeat Captain Qwark's Ship
Use a Sand Mouse to destroy all the tanks on Batalia
Turn a tank into a chicken on Rilgar
Obtain the Persuader
Score 4500+ on a hoverboard race on Kalebo III
Destroy all cargo ships in the base on Orbital Oltanis
Traverse the water region without losing any health on Veldin's Orbital Station
Kill 10 elite guards with only the wrench on Veldin