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