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