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