Here are the average scores that Ryo will post when you challenge him, so all you need to do is build or purchase a machine that will destroy these scores.
Ryo's scores (on average).
Drag 1/2 mile: 19secs
Wheelie: 600 meters +
Speed trap: 150 - 160 km/h
Drift: 3500pts +
The other races you simply have to beat him to the checkpoints or the finish line.
Drag 1/4 mile + 1/2 mile: Zonda 6.7s and 10.6s respectively
Drag wheelie: Zonda 1300 meters. Hit turbo at 3rd gear. Easy!
Speed: Supra with a Ford GT for speed trap challenges.
Drift: Rx8 avg 5000pts without much effort.
Grip: 911 (NOT the GT2!)
Just purchased the best power + traction parts for my cars and for the Supra and 911 lowered the ride height to the lowest, and a wide body kit with maximum downforce. Other than that, no need to tune.
The only problem I had was with the damn "catch-up" feature. On the speed challenges I was constantly slowed down to 140 or 150 km's, when I hit nitro I'd get slowed down to 160. My Supra is more than capable of hitting 180kmh's +.
I played the entire game on casual. By lowering the assists, you also increase the difficulty. No point in making this game harder for yourself! :)