This may seem like a daunting task, but even I (who can barely scrape a win together on Skilled difficulty) managed to complete it.
Enter Racebox and set up the following:
Race Type: Tournament
Speed Class: Venom
Weapons: Off (this is the important bit)
Hit X, then pick a track you're comfortable with and add it to the Tournament eight times using the Square button. I used Anulpha Pass (Forward) - hey, if you're going to attempt to Beat Zico, you need to know it pretty well ;) I then chose one of the Icarus racers - Anulpha Pass is smooth enough that you don't need decent handling, and the top speed of the craft helped me.
With this setup, I found races pretty easy to win - most of the time I could finish the first lap in 4th-5th place, and by the end of the second lap I was either 1st or 2nd. It helps to take the "high road" in Anulpha Pass (the elevated straight bit), though I'd avoid it on the first lap if it was crowded. I also managed to squeeze in a barrel roll most of the time, which is a nice little speed boost - just try not to boost into the back of one of the AIs.
Just make sure the Weapons are off, and you should be fine :)