Kaizo 1 - Level 1
Yoshi's Island 1
The Bullet Bill Tower
Right off the bat, you are going to need to be running in either direction to increase the height of your jump to bounce off the top Bullet Bill. If you immediately clear the tower, the cue for the next launch occurs right after the timer hits 395. Alternatively, you can practice using an audio cue. For this jump, try to hit the top Bullet Bill as far right as possible, and hold B the entire time.
After clearing the Paratroopa jump, drop down to the bottommost block and jump straight to the second chuck in one motion. This will ensure that the Chuck will not leap while you are in the air. Bounce off the second chuck to the block right before the Para-Goomba.
After dodging the hidden block and clearing the Para-Goomba, some Bob-ombs will be marching towards you. To clear them, come to a complete stop, or near-complete stop and orient your controller so that you can quickly (2 frames (33 milliseconds) or less) press the A button and clear the Bob-omb without touching the Munchers above.
The Chuck/Muncher Trap
If you died in the second half of the level or were unable to damage boost past the Chucks, they can be tricky to clear. The first Chuck can be cleared by jumping on top of the stacked blocks with A or B, making sure you hold the jump button when you land on the blocks. This will allow you to simply run (with X or Y + the jump button) across the gap with the Chuck underneath.
There are a few ways to get past the second one. If you manage to clear the first Chuck and run underneath the Piranha Plant in one motion, you can (while still running) lightly tap A to do a short spin jump off the edge of the pipe and briefly release the dash button to avoid the first Muncher. If done correctly the Chuck will have jumped so that your momentum can take you underneath. Otherwise you can line up about a block and a half left of the first Muncher, begin jumping when the Chuck begins his mini jump, and run underneath the Chuck. It may take some practice to optimize timing, jump height, and speed. This is a recurring trap that will make several appearances during the series.
The Piranha Plant/Muncher Drop
There are two ways to get by this one. If you choose to spin jump off the Piranha Plant, make sure your timing is right to land on the bridge underneath. A good cue for a workable jump is when the Piranha Plant jumps about the same time the bridge opens. More importantly, don't jump down until you can gauge either 2-3 bounces (depending on preference). Regrab A after your final bounce, as it will give you the best chance of clearing the lower-left Munchers while staying below the upper-right Muncher.
If the bounce method doesn't work for you, place Mario's heels on the edge of the ledge and wait for the bridge to open. As soon as it starts to open, only press right, then roll your thumb from Y to B when Mario is exactly one block height above the upper-right Muncher, making sure you are still holding right and Y when you get to B. Timing may vary depending on your television.