Here is the full list of all 20 Daytona Racing achievements.
Ride 1 circle
Hit the thorns
Change the line very close to another car
Hit the oil
Crash on 1st lap
Hit the slow down penalty
1st crash
Ride 1 lap on eight map
Avoid crash by hitting the oil
Cross the finish line
Ride 5 laps on circle map
Ride 10 laps on circle map
Ride 15 laps on circle map
Ride 20 laps on circle map
Ride 25 laps on circle map
Ride 5 laps on eight map
Ride 10 laps on eight map
Ride 15 laps on eight map
Ride 20 laps on eight map
Ride 25 laps on eight map