You basically need to have a knack for knowing (or feeling) whether or not you're going through a turn as fast as you think or feel you could be.
For instance, on the very beginning U-turn, I used to think drifting through that would be relativity quick, but then I tried gripping through it and that was even faster. Then I tried cutting through the grass in hopes I would shave even more time off, but it turns out there's a drop on the terrain which leaves me airborne and bouncing so that wasn't a good idea.
When I hear the car drop in power through a turn, or if it's just redlining through it, I instantly feel like that turn could have been taken much faster and then I try different braking times, different lines, until I find one I feel is best.
You know that 1st right turn you take? At first I stayed on the dirt because if I touched the apex of that road, the car hits a bump and loses control. Well, I tried cutting in the grass between that bump and the tree and realized I could hold a much higher speed through that passage until the upcoming left turn if I went with this.
Also, don't slide your car excessively. If you aren't and still can't match my time, then you must be braking more than you need to for certain turns. Makes sense, no?