Here is the full list of all 14 Rush VR trophies - there are 11 bronze, 2 silver and 1 gold.
Come 1st in 5 Races
Fly through a waterfall
Come 1st in a Multiplayer Race
Beat your ghost in a Time Attack course
Thread the needle
Come 1st in any Race
Grind for 15 seconds
Grind for 60 seconds
Win Gold in all Verdant Valley Races
Win Gold in all Frozen Alps Races
Win Gold in all Sunburst Canyon Races
Win Gold in all Misty Mountain Races
Win Gold in every Race
Earn 500k points across all Score Challenge courses