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