Here is the full list of all 35 Riders Republic trophies - there are 15 bronze, 15 silver, 4 gold and 1 platinum.
Complete a Shackdaddy Weekly Challenge
Land a tricks combo worth 75,000 points or more
Reach Weekly level 2 in the Multiplayer Competition
Earn 25 different gears
Perfectly land a 1080 spin (or superior), with tricks landing set on Manual
Add a new sponsor
Collect 11 stars to unlock the Riders Ridge
Obtain all other trophies
In solo, finish first in 8 big events in snow careers
In solo, finish first in 8 big events in bike careers
In solo, finish first in 4 big events in air career
In solo, complete the snow tricks boss event
In solo, complete the snow race boss event
In solo, complete the bike tricks boss event
In solo, complete the bike race boss event
In solo, complete the air career boss event
Complete 50 Mass Races
Discover 15 Landmarks
Welcome to the Red Bull Family! Complete a contract for Red Bull
Complete 100 sponsor contracts
Capture 100 modules in Tricks Battle
Capture 30 districts in Tricks Battle
Score 5,000,000 points with the one-foot board
Complete 10 Versus Mode Events
Perfectly land 50 double backflips or more, with tricks landing set on Manual
Complete 100 different Events
Earn 250 Stars
Complete 50 UGC events
Complete 100 Events without using the Backtrack
Complete 50 Events with Funkies
Complete 10 Shackdaddy Weekly Challenges
Complete 50 Free for All sessions
In solo, finish first in the Invitational
Complete 20 Stunts
Find 200 landmarks, relics or collectibles