This page is intended to list the various known time-saving tricks in Yoshi's Story.

Yoshi's speed behaves in a way that can be abused in this game. When you start walking after Yoshi's speed hits 0, it follows a pattern like this {.45, .9, 1.35, ... , 4.05 , 4, 4, 4, ...}. Essentially, your speed increases by .45 per frame. Eventually you will obtain a speed value which is greater than 4.0. The intended speed cap is 4.0, so the game adjusts your speed on the next frame to match this. This can be easily abused though. By holding no left or right directional input and jumping on the frame your speed hits a value over 4.0, your speed will remain over 4.0. This can also be done while you are in the air, but your speed increases by .23/frame, so it is generally faster to accelerate while walking if possible. An important thing to note is while in the air, even if you release input after getting a speed of 4.0, it will slightly decrease from whatever value you obtained. Thankfully, there is a way to avoid this loss described below.

When Yoshi starts moving from 0 speed, the fastest method of acceleration is walking until your speed hits 4.05. You then want to jump 1 frame on this frame. Additionally, you will want to be holding left at an angle of about -51 (can sometimes be an angle closer to 0). After a few frames of holding this angle, Yoshi's speed will drop just below 4.0 to something like 3.998. On the frame you get this speed, hold right for 1 frame. Yoshi's speed will jump up to around 4.228 which is the max speed that can be obtained while Yoshi is in the air. On the next frame you need to do one of several things on that frame to prevent the speed from slightly dropping:

These will all keep Yoshi's speed at the original max value.
When Yoshi lands from being in the air though, it is possible to further increase his speed. By holding left for 1 frame, followed by no input on the next frame, followed by holding right on the next frame, you can get Yoshi's speed up to 4.448. Generally the frame you want to start this series of input is two frames before you hit the ground. In some weird instances this won't work and you have to hold left for 1 frame followed by right for 2 frames to get the desired result. In an even rarer instance when neither of these work, you can get up to max speed by holding left for a frame dropping Yoshi's speed below 4.0 by some amount. Then, depending on what your speed is, you need to hold left at a specific angle (the angle will vary, while my speed was 3.91 I needed to hold -47) for one frame. The next frame you want to hold right. If you got the correct angle, Yoshi's speed should be just below 4.0 at something like 3.99. Continue holding right on the next frame and his speed will hit max. Ideally anytime after you max Yoshi's "air" speed, you should max his "ground" speed as early as possible.

If you throw an egg while you are in the air, it will cause Yoshi's speed to drastically drop for a few frames. If you are on the ground though, you can maintain a speed of 4.0 while Yoshi is aiming the egg. To get you speed back, you need to jump for 1 on the first frame where Yoshi's speed doesn't drop below 4.0. Additionally, you will want to hold left at an angle of -29 until Yoshi's speed drops to around 3.99, then accelerate to the maximum "air" speed as described above.