Here is the full list of all 31 Rush Rally Origins achievements.
Hit over 500 objects
Finish first in 6 championship rallies
Unlock 5 cars
Get a medal in 6 championship rallies
Finish first in a championship rally
Finish any stage without hitting anything
Finish any stage without going off the track
Get a gold medal on a Race stage
Get a gold medal on a Time Trial stage
Get a gold medal on all stages of a Time Trial rally
Upgrade a car to A-Class
Upgrade 8 cars to A-Class
Unlock all the upgrades for a single car
Unlock all upgrades for 8 cars
Unlock weather on 6 Time Trial rallies
Unlock weather on 6 Race rallies
Unlock weather on all game modes
Get a gold medal in time trial without using corner arrows
Get a medal on all stages of 6 rallies in Time Trial
Get a gold medal on all stages of 6 rallies in Time Trial
Get a gold medal on all stages of a Race rally
Get a medal on all stages of 6 rallies in Race
Get a gold medal on all stages of 6 rallies in Race
Get a gold medal on any stage without hitting anything
Get a gold medal on any stage without going off the track
Drive over 500 km
Drive over 1000 km
Hit over 1000 objects
Login to Rush Rally Online and view the leaderboards
Download and race against a competitors ghost from the leaderboards
Download and beat a competitors ghost from the leaderboards