This was originally written on Niconico's Blomaga, but since the service ended and I hadn't updated it with new techniques, I'm now putting it all together again here.
Super Mario Sunshine runs at 30 FPS, but internally, each frame is further divided into four parts.
TAS (Tool-Assisted Speedruns) adjust Mario's position and velocity so that he lands or touches walls at the most advantageous of these four subdivisions.
There are methods to adjust height, such as changing Y-velocity with a shotgun (water spray technique) or altering the timing of the hover.
For wall kicks and QF, even if you perform a wall kick on the same frame, adjusting which QF Mario enters the wall-slide motion can change the starting height of the wall kick.
If Mario’s vertical (Y) speed before touching the wall is positive, then touching the wall at the latest possible QF will maximize height gain. If his vertical speed is negative, touching the wall earlier helps minimize height loss.
This refers to jumping while Mario already has some speed.
The speed that carries over into the jump is 80% of Mario’s previous speed, except for the triple jump, which retains 100% of the speed.
The more Quarter Frames (QFs) Mario spends grounded, the more his speed decreases. For example, when recovering from a dive on flat ground, only about 60%–70% of the speed is preserved. However, this can be resolved by using shotgun techniques to adjust the height.
You can judge how much speed is retained by looking at Mario's landing animation. If he lands while maintaining his previous posture, the timing was ideal. If his posture breaks—like leaning forward—then some speed has been lost.
The shotgun (a quick burst from FLUDD) affects Mario’s vertical (Y) velocity.
Whether it increases speed depends on the direction of the nozzle, but in most cases, it results in increased vertical speed.
When you want to intentionally reduce Y-speed to shorten airtime, it’s combined with an upward-facing shotgun.
If you press the R button for 1 frame before performing the shotgun input, the water spray fires diagonally upward.
This input is essential for quickly defeating Shadow Mario and for erasing the M-shaped graffiti on the ground.