Before being able to challenge Darius, you must race Wolf, Kenji and Angie in their new rides: Wolf: Lamborghini Gallardo; Kenji: Mitsubishi Evolution; and Angie: Plymouth Hemi Cuda. You will have to defeat them in the canyon first and then the city. Both races are sprints. After you defeat them, you will be able to challenge Darius in his Audi Le Mons Quattro. You will not be able to switch cars before each race. Start with the car that you want to use for all four races. The car needed to defeat Darius is a Tier 2 Tuner since they are the best at turns (Canyon Duel). Kenji's Mazda RX-7 is the best car if it is tuned out to the maximum. However, if you did not acquire the pink slip from Kenji, then your best Tier 2 Tuner should be fine, as long as its tuned fully. Defeating Darius will take several attempts, but you will eventually get used to the roads and will be one step ahead of him, making your chances of winning larger every time you race him. Also, if you cannot make it past the first, second, or third race, enable the "Unlimited nitrous" code then hold down the nitrous for the entire race, except for sharp turns. You should have a fairly easy win as long as you take all of the shortcuts. If you miss one shortcut, Darius will take it and you will be in last place.
Get the Mitsubishi Lancer and tune it fully for all race package transmission, engine, nitrous, and supercharger. Also, enable the "Unlimited nitrous" and "Unlimited SpeedBreaker codes" When racing Darius, drive a normal race but use nitrous the entire time. In the canyon, stay on the pedal the whole time and only use the brakes if you have to. There is one point in the race at about 63% where there is a wall instead of a guardrail. When you get there, floor it to possibly pass Darius. If you do not, you will earn around 10,000 points anyway and still have a good chance at winning.
To defeat Darius in Canyon Duel, try to get in front of him. After that, stay in front of him for ten seconds and you will win. This also works with all other Canyon Duels. Pulling away and making him fall off also works.