In dirt racing, "winning a race" is when you finish first in the A-main. So you must qualify, run the heats, and the qualfying sprints, before you can enter into the A-Main. You can do this in quick race or career. It should also work in multiplayer, but just a quick race with a short race length on the easy difficulty will surely lock this cheevo up for you. The cheevo should pop after exiting the post race screen, and returning to the main menu after the tenth win. Happy hunting!