Here is the full list of all 37 Ratchet & Clank Future: A Crack in Time trophies - there are 25 bronze, 6 silver, 5 gold and 1 platinum.
Collect all trophies in the game.
Complete a Challenge Mode playthrough.
Vanquish Lord Vorselon.
Collect all gold bolts.
Collect all Constructo modifications.
Rescue all Zoni.
Complete all space missions.
Complete the game on Casual.
Complete the game on Medium.
Complete the game on Hard.
Defeat General Azimuth and save the universe.
Collect 1,000,000 bolts.
Defeat Dr. Nefarious.
Stop the Agorians from destroying Gimlick Valley.
Destroy Dr. Nefarious' armada.
Purchase all GrummelNet Weapons.
Visit the Insomniac Museum.
Win the Raritanium Tournament.
Reunite with Clank.
Unlock the Orvus Chamber.
Save General Azimuth from Lord Vorselon's clutches.
Confront Dr. Nefarious in the past.
Find the Obsidian Eye.
Collect 250,000 bolts.
Win the Gold Tournament.
Upgrade one weapon to level 5.
Win the Silver Tourament.
Win the Bronze Tournament.
Score 10,000 points on My Blaster Runs Hot.
Repair temporal damage caused by Dr. Nefarious.
Destroy the VX-99.
Master the hoverboots.
Collect 50,000 bolts.
Defeat the Hypersonic Brainwave Scrambler
Collect 10,000 bolts.
Retrieve Chief Zahn's Zoni Vessel.
Complete Great Clock, Sector One.