Clipping Points appear only in tandem events, therefore you can't progress in this achievement if you're playing the singleplayer Drift events. You can either play Tandem, which is against the AI, or do it much easier on your own leisure in Multiplayer.
You can do this in any map, but the best one I've found is West Coast Arena, which costs $400.000 though. It has very short tracks and they're easy to figure out.
Go to Multiplayer, then Room List. Press

to creat your own room. Change the track to West Coast Arena. Leave the rest of the options as they are, aside from the very last one, Password. Change it once with the d-pad and it'll automatically generate a password for your room. This ensures you get no randoms. Press

to create the room.
As soon as you spawn in, press up on the

, then change the first option to "Duel", then the Players option to 1 and the Clipping option to B. This also the set-up used for the 1000 multiplayer wins achievement:
On the first right hander, right on the banking you're starting on, there are some brightly colored lines close to the left wall, with objects that resemble anti-parking ballards at the end of each one. In order to get points from hitting the Clipping Points, you need to drift as close as possible to the ballards, without touching them. You don't even have to be that close. Each line is seperated in three equal parts. Just make sure that your rear axle goes over at least the first of the three parts each line has.
Once those are done, the track continues to the right and in the infield part of the map. There are a few more clipping point on the right side of the final left handed turn which gets you to the end of the track. Make sure you brake and go easy on the speed and you should also be able to score some points from that part of the track too.
Finish the event, press

on the results screen, then press

and then

to reset the event. Rinse and repeat. Don't even bother restarting if you hit or miss a lot of clipping points, as you'll be working towards the 1000 multiplayer win and the drifting and driving mileage achievements.