Start Time Attack, pick any car (I did it in the Enzo but everything will hit 300), Tuned so you have the 300km/h top speed.
After the opening stage, bear LEFT at the first junction so you enter the 'Bay Area' stage (like you were going for Goal A). DON'T drift around the first bend after the sky changes colour! Maintain your speed around that corner, and around the next corner onto the bridge. The achievement should unlock at the other end of the bridge just as you're forced to drift around the S curves.
It seems that while your car will maintain 300km/h while cornering (even with the tires smoking), if you straighten out too quickly you drop for a split second to 299km/h which seems to spoil your run. So, gentle on the steering as you straighten out!