Here is the full list of all 23 NASCAR Arcade Rush achievements.
Customize all available parts on a single vehicle
Reach XP level 75
Compete in 25 Quickplay races
Win a Quickplay race on all 12 tracks
Compete in 10 Quickplay races
Win all 9 Cups on any difficulty
Win all 9 Cups on Rookie difficulty
Win 10 Online Cup Series
Reach XP level 50
Reach XP level 25
Win 4 Cups on any difficulty
Compete in 25 Online races
Compete in 10 Online races
Win 2 Cups on any difficulty
Complete your first Cup Series on any difficulty
Win your first Cup on any difficulty
Win a single Online Cup Series
Compete in a single Online Race
Compete in a single Quickplay race
Win all 9 Cups on Elite difficulty
Beat a single Gold Medal times on Time Attack
Beat all 12 Gold Medal times on Time Attack
Reach XP level 100