Horizon Chase Turbo

The first thing you can do on the game is to race on the California stage. There are three races there (plus an upgrade one).
As soon as you complete your first race, your ghost will be saved.
You will progress through the game unlocking upgrades and cars, then, you can go back to that first race, and by default your ghost will be enabled (you can disable with [Y]). You only have to race better this time and beat your ghost, and when the race ends the achievement will pop up.