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