I am a newbie with regard to drifting (and driving in general) and had some difficulties clearing this challenge. Nevertheless, I managed to clear it after a few attempts. Here are my assist settings:
Traction & Stability Control: Off
Damage, Fuel, & Tire Wear: Cosmetic
I used 1997 Lamborghini Diablo SV. Basically when you are approaching a curve, press A to hand brake and at the same time steer to the direction of the curve to start drifting, and while drifting, use steering and throttle to maintain composure of the car to continue drifting. Drift points seem to accumulate faster when you maintain a bigger angle.
The course has various unmarked sections around curves and only in those sections you can accumulate drift points. When you drive over a section you cannot turn around, drive back, and attempt it again (no drift point will be awarded if you try to do so), though you can always use Y to rewind. One curve can have multiple sections and I found it helpful to drift in one section, brake (to not enter the second section), turn around and drive back, approach the curve again, skip the first section and start drifting in the second section.
You need to have at least a few "good drifting" in one lap to reach 25000 points.
I know I am by no means good at drifting, but I hope that by sharing my experience, I can at least help a few people who are also having difficulties clearing this challenge.