After trying the Course D for months, i've tried another courses and, for me, the easiest way is to use Course A, turning left for every junction.
First and Second Stages are exactly as described by Dodgymat.
On the third stage, just slow down a bit to "run through the blue". Run and slow down again to "hit the blue cones". The third special request here is to "Keep passing cars", and you probably will not have any problems with that.
The fourth stage is simply to beat the red cars. Just do not hit any car and, if you did "Passing Breeze" or "Gunball King" achievements, you probably will not have any problem here.
The fifth stage is the tricky one. To "hit the blue cones" and "pass through the gates" you just have to slow a bit. The problem is the final task, "drift and hit the blue cones". You have to put your car on the right and start to drift perfectly hitting the cones. It's tricky, but with practice you can do it.
Here, you will just have problem with one drift, instead of the annoying Ice Scape stage.
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Sorry for my poor english, it's not my native language.