If you don't do it already, race with the view set so that you can see your speed. For some reason you move faster when drifting, so try to zigzag while always drifting when possible. Also remember that having more bananas makes your boosts last longer, so try to round up a bunch of bananas on lap 1 then focus more on hitting zippers in later laps.
Also, Fossil Canyon, depsite being one of the first tracks, has one of the hardest TT times to beat, so don't give up, just skip it and do easier ones.
Also, if you just can't beat it fair, tapping A makes you go faster than just holding it down.