Here is the full list of all 23 Ratchet & Clank: Into the Nexus trophies - there are 8 bronze, 7 silver, 7 gold and 1 platinum.
Collect every trophy in Ratchet & Clank: Into the Nexus.
Upgrade all weapons to level 6.
Beat the game in Challenge Mode.
Beat the game on Legend difficulty.
Beat the game on Hero difficulty.
Purchase all armor.
Collect 1,000,000 bolts over the course of the game.
Upgrade 1 weapon to level 6.
Beat the game on Cadet difficulty.
Defeat the Nether Leader and banish his kind.
Complete all Netherverse segments.
Scare at least one of every type of enemy using the Nightmare Box.
Collect 200 raritanium over the course of the game.
Collect all Gold Bolts.
Purchase all weapons.
Unlock the vault on planet Thram.
Win the Destructapalooza Gold Cup.
Form an alliance with Neftin Prog.
Defeat Neftin Prog.
Win the Destructapalooza Silver Cup.
Win the Destructapalooza Bronze Cup.
Beat Pest Control with just the Omniwrench.
Grav-Leap to the Thug ship circling the Nebulox Seven.