Just a quick solution for this achievement
Firstly pick Rivals, then Spec Challenge and then it is the second option
You are automatically put in the McClaren P1
This time DOES NOT have to be a clean lap, so if you don`t take a corner cleanly or you think you can do it faster , you can rewind to your hearts content, till your happy with it.
I had a practice lap from a standing start and fell 12 seconds off the pace, then on a flying lap managed to beat it (with a lot of rewinds), and to give you a bit of help you can watch the split times to see how you are progressing compared to you previous best time.
Hope this is of some help to you
EDIT as mentioned in the comments by gsoria , you will have to upgrade the P1 and that the LCE is not eligible for this Rival Event /
A good timesaving tip from Hanrec2, if you reverse at the start as far back as the last bend, then accelerate over the line, the clock restarts when you cross it. This tip would negate the need for a practice lap.
Feel free to follow AvengedAgainst`s time and stay just behind him or obviously in front for the achievement.
Thanks for the tips guys