There are three career majors on Gotham arcade. Asia, North America and Europe.
You must win the three during your seasons' play-trough.
Actually the first two are quite easy. You can win them using a bike, which i think is pretty easier to control.
The real problem is the third one in Europe. For this one, you must not use a bike, since its top speed is way below than the other cars which are surely going to overtake you. So for this one choose a car with good top speed and grip, so you can control it when turning. The key point is to stay ahead of them all time, this way they will have to reduce when trying to overtake you.
If you did this correctly the achievement should pop at the end of the third career major you win.
A little tip if you beat to number #1 and still don't have this achievement. You can skip the other tournaments and only go for the majors. When choosing a tournament, always choose the one with quickest first task. Normally, it is elimination, because you can stay still and be eliminated quickly. Then, choose the option to save and go to menu. When you return to menu and go to your career, you will be given the opportunity to abandon championship and skip ahead. So keep doing this until you get to the major, win a track and then save.
If you're no sure if your choice of bike or car is good, you can always make a backup of your savegame on an usb stick, try it, and then recover if it was not a good one.
Hope this helps.