Credit to AceCardJones on TA for this one...
Once you have the Egg Hanger track unlocked go to Single Race and select it. Choose Medium difficulty and Sonic with Standard Mod.
Hang back in 8th place from the start but not too far behind. After the initial straight you go into a long left hand bend and can drift past your opponents. You will probably get past five before the bend switches to the right, if not you can quickly switch direction by briefly letting go of the left trigger.
If you don't get it on the first lap, restart the race, the other racers will be too far apart for this to work on the 2nd lap. I got this on my 2nd attempt using this method.