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.
Save General Azimuth from Lord Vorselon's clutches.
Collect 250,000 bolts.
Confront Dr. Nefarious in the past.
Win the Bronze Tournament.
Find the Obsidian Eye.
Upgrade one weapon to level 5.
Repair temporal damage caused by Dr. Nefarious.
Destroy the VX-99.
Collect 50,000 bolts.
Master the hoverboots.
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.
Unlock the Orvus Chamber.
Defeat General Azimuth and save the universe.
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 Silver Tourament.
Win the Gold Tournament.
Win the Raritanium Tournament.
Complete the game on Medium.
Rescue all Zoni.
Collect all gold bolts.
Collect all Constructo modifications.
Complete all space missions.
Vanquish Lord Vorselon.
Purchase all GrummelNet Weapons.
Collect 1,000,000 bolts.
Complete the game on Hard.
Complete a Challenge Mode playthrough.