Here is the full list of all 33 ONRUSH trophies - there are 19 bronze, 7 silver, 6 gold and 1 platinum.
Earn 100 Gold 'GAME TIME' Medals
Superstar - Win the Founders' Trophy
Perform 1000 'NEAR ALLY' actions
Superstar - Unlock 'Superstars'
Perform a 'VOMIT COMET' action
Play 10 COUNTDOWN Matches
Play 10 LOCKDOWN Matches
Feature in the player spotlight 10 times
Play 10 SWITCH Matches
Reach player Level 30
Earn 50 'HUNTER' Medals
Superstar - Unlock 'Snowbound'
Play 10 OVERDRIVE Matches
Reach player level 15
Personalise all 8 Classes
Superstar - Unlock 'Starpower'
Earn 10 Crashtags
Superstar - Unlock 'Regeneration'
Reach player level 5
Superstar - Unlock 'Uprising'
Smash 5 Tombstones in a single match
Superstar - Start 'Origins'
Perform a 'CRUSHED!' Takedown
Rush for the first time
Takedown an opponent!
Introduce yourself to the fodder
Use boost for the first time
Obtain all trophies in ONRUSH™
Personalise all 12 Characters
Collect 250 or more Gear Items
Earn 5 Ubertags
Earn 50 'CHECKMATE!' Medals
Superstar - Max out your Superstar Rating