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 all space missions.
Complete the game on Medium.
Complete the game on Hard.
Complete a Challenge Mode playthrough.
Score 10,000 points on My Blaster Runs Hot.
Collect all gold bolts.
Visit the Insomniac Museum.
Vanquish Lord Vorselon.
Rescue all Zoni.
Collect all Constructo modifications.
Win the Raritanium Tournament.
Win the Gold Tournament.
Win the Silver Tourament.
Complete the game on Casual.
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.
Reunite with Clank.
Unlock the Orvus Chamber.
Save General Azimuth from Lord Vorselon's clutches.
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.