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 Constructo modifications.
Visit the Insomniac Museum.
Vanquish Lord Vorselon.
Rescue all Zoni.
Complete a Challenge Mode playthrough.
Complete the game on Casual.
Complete the game on Medium.
Defeat General Azimuth and save the universe.
Collect 1,000,000 bolts.
Defeat Dr. Nefarious.
Win the Raritanium Tournament.
Stop the Agorians from destroying Gimlick Valley.
Destroy Dr. Nefarious' armada.
Purchase all GrummelNet Weapons.
Reunite with Clank.
Unlock the Orvus Chamber.
Save General Azimuth from Lord Vorselon's clutches.
Win the Gold Tournament.
Win the Silver Tourament.
Confront Dr. Nefarious in the past.
Collect 250,000 bolts.
Find the Obsidian Eye.
Upgrade one weapon to level 5.
Win the Bronze Tournament.
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.
Collect all trophies in the game.
Score 10,000 points on My Blaster Runs Hot.
Collect all gold bolts.
Complete all space missions.
Complete the game on Hard.