Final Exam: Off of the first jump, try and land early on the wobbly bridge at a roughly 50 degree angle, then upon landing try and convert as much momentum as you can horizontally, hold right on dpad for maximum velocity to jump over the cheese guards. Collecting the spirits lowers the bridge on the right side so just complete normally from this point.

Boy Meets Girl: A powerful jump off of the first ramp can allow you to overtake Peri immediately.

Fishy Business: The first of the goal chase levels, which all have speed tricks. For this level, shortly after starting lightly tap left on the dpad, and upon nearly catching up with the goal, hold hard left to finish 1 frame faster (you can tell as you'll get a 3.766 instead of a 3.783)

Eggoland: Upon collecting the first set of sticky tires, immediately activate them, reverse around to the right side of the floating platform and deactivate to fling yourself over the lip to save a short amount of time.

Desert Storm: With enough speed, you can jump over the rocks at the end of the level from the ramp, saving about .75s with good traction.

Manic Miner: With a good path through the fossil, a large enough bounce can be achieved off of the top of the hill to bounce over the trigger breaking the bridge. If this is failed, the gap can still be jumped without using a spring. Saving the spring is done to get a much faster jump after the explosive gate; there may be a better place to use it but I haven't found one.

The Trap: You can hit the right trap release in the initial fall to save a short amount of time.

Pipe Dreams: You can chain the first boost used at a specific angle into the second boost to jump up to the top of the next cliff, saving a significant portion of time.

Slippery Slopes: Same idea, except you chain a boost into itself. You cannot immediately regrab a powerup upon usage, so you must use the boost just before it respawns to collect it again.

Platformer: With a full run up and a lean left at the end of the platform, it's barely possible to bounce off of the hover platform and make the initial jump, saving about 2 seconds. At the end of the level, it's also possible to use the spring to just jump the gap to the right, saving another couple of seconds.

Catch Up: The second goal chase level. At the end section, get enough speed going off of the small bump to jump off the end of the ramp into the goal- I find that holding right and then left at the lip helps immensely.

Addendum to Catch Up. I've discovered a faster strat. Upon reaching the first purple tunnel, if you flip your car onto its roof (done most easily by driving slightly into the tunnel, losing all your speed, and then accelerating whilst leaning left), you can get a good enough bounce from righting yourself that you jump straight into the goal. Sub 10s (9.733 from my testing) is possible with this, but the strategy as it stands is wildly inconsistent.

Moon Mayhem: With a good enough run-up to the triple jump ending, you can get enough speed to grab onto the walls earlier, reducing air time and allowing you to start accelerating sooner. Done 3 times, it saves at least half a second.

Goal Grab: The final goal chase level. With a very precise jump, it is possible to bump your back wheel into the explosive at the start and convert enough momentum from it to jump into the goal, saving over 30 seconds.