The N-Dura Cup is in the Championship menu, and is the first one there.
You can win it by setting the AI to Easy, and since you need to complete 10 split-screen Championships anyway, you can hook up another controller and take up one of the AI slots with a car that just stands there. (If you've got a giant TV and don't mind playing on a quarter of it, you can hook up four controllers.)
The championship consists of 4 races with 3 laps each. The races use the regular versions of the tracks, not the mini ones they use in the career championships.
I would post further tips but with the AI set to easy, this is such a breeze that you won't need any.