This should not pose too much of a problem. Simply set up a Grand Prix at Turkey and make sure you are driving as Lewis Hamilton.
If you are confident enough you can set the race mode to race only and the distance to one lap.The grid order is randomized, although Hamilton will not start any lower than 6th, so overtaking all the cars in one lap should not be a problem. If you are having problems, either set the A.I. difficulty to Amateur or increase the race distance.
Note: The title of this achievement is a homage to the 2011 Turkish Grand Prix, where Lewis Hamilton passed Jenson Button time after time only to be re-passed shortly after - until finally overtaking him for good and securing 4th place.