Here are a number of tips on ways to improve your run times. Feel free to add to it if you find any good strats.

General: Press the X in the bottom right corner of the screen AFTER crossing the finish line and the screen fades to black once, to avoid the pet feeding screen and spending pet energy. You must wait for the screen to fade after crossing the finish line, or the game will crash.

Trial 1: You can run straight through the first mallet without stopping (if you get a good cycle), despite it looking like a close shave. If you don't, reset until you do.

Trial 2: The pistons at the end have a consistent cycle you can use to get through them. Stick to the right side and just go over the pistons that don't shake.

Trial 3:

Trial 4: There are two pistons at one point in the Trial that have a slightly larger than normal gap between them. Meaning you can slide between them, even though you normally would have to wait. They are on the left side of the track before some spinners and mallets.

Trial 5: