1-1 Any%

Basics

A straightforward level that does not require any particular egg count.
Make sure not to run on any of the small hills in the terrain.
An enemy can be used for an Extended Flutter, which gets Yoshi high enough to make it over the middle of the level, removing the need to take the slow beanstalk.
An easy way to kill the pirahna plant at the end of the level is to fire a neutral eggshot (simply tapping A if your controls are set to Hasty) in the air or just before running into it (simply tap A twice if on Patient Settings).
In this level, collecting a flower and getting hit by an enemy will both trigger an information box, which will waste a little bit of time.

Faster Shyguy Bounce

This strat saves about 0.4s over the basic route.
You upspit the enemy without holding right so it lands in the correct position. Shooting the green shyguy out of the way makes it much easier.
If the shyguy lands in the wrong place you can still do the basic route as a backup without losing any time.

1-1 IL WR

There is a small optimization that can be made which requires a perfect jump chained with an extended flutter to skip the beanstalk. It can be seen in the Individual Level World Record.
Do the faster route shown above, but after you bounce off the enemy do a perfect jump off of the rotating platform to keep your extended flutter.
This saves about another 0.4s over the strat shown above.

If you miss it, you can get up using this backup involving a perfect flutter (hold B when you bounce off the enemy to bounce higher).