Warps and Warpless
A couple of tricks turn this normally complicated and lengthy level into a very straightforward and short one. First, gatehacking saves time over the using the stairs:
For this reason, it's ideal to enter 2-4 with at least one egg. If you don't have one, though, you can easily fetch one at the beginning of the second screen by lining Yoshi up underneath one, holding up, and then pressing Y and rolling your thumb down to B. Yoshi's fully extended tongue will clip through the wall and grab the egg.
After the gatehack, a perfect flutter skips a large chunk of the level:
If you struggle with perfect flutters, a common simpler strat is to use one of the ghost shyguys to perform an extended flutter instead:
In the warps category, running along the ghost enemies into the horizontal pipe at the end of the second screen triggers a 1-1 warp glitch. Doing the warp skips the boss, and saves about 20-25 seconds.
An egg should be used on the first flower if you have at least 2 eggs. To do the ghost room, run to the right, grab the two eggs, then run to the left and fire an egg just before hitting the wall. This will kill both ghosts and put you in position to grab the flower immediately.
After the gatehack, the key grab section can be quite tricky. The easy way to do it is to hit the red switch, and easily shoot the key cloud, then use a shyguy to boost up to the middle tunnel and proceed to the left.
The more difficult but faster method involves spitting a shyguy up against the roof, fluttering over the lava while shooting the key cloud, then using a tongue tongue followed by repeated spammed tongues to acquire the key. If done quickly enough, the shyguy will be perfectly positioned after this to allow an extended flutter to reach the middle tunnel path.
To get the last flower, stop in the position indicated in the image below, wait about .5-1 second, hold left, then immediately fire a neutral egg.