Play Like Donkey Kong in Time Trials
One of the less-obvious things about Crash Bandicoot is that the levels are set up very similarly to the Donkey Kong Country games on SNES. What this means is that obstacles will have a certain rythym to them, so that if you run through without stopping, things will just happen to line up so that you won't have to stop.
This is an important factor to wrap your head around when doing Time Trials, because being just a little bit too slow will mean that you'll be out of sync with everything, making it much more likely that stuff will just be in your way all the time.