Try to bring six eggs into this level. It is possible to clear out the first ghost without slowing down at all but you may want to slow down a bit to be safe.
Tonguing forward before walking through the fish slows you down just enough to allow you to walk through it without getting eaten.  Do not shoot the fish as it can softlock the game, and your egg would be better used elsewhere anyway.
The first video gets full eggs from the egg block, although you technically only need 3 if you do the egg grabs in the IL record and shoot the boss first try.
Water hallway comparison: 
The big ghosts can be killed with a single egg shot by shooting them as they are scrolling on screen. The easiest way to do this is to come to a complete stop at the spot shown in the top video, then tap A and hold right at the same time. Letting go of right but not completely stopping (shown below) is faster but more difficult.
At :56 in the first video, wait until Yoshi emerges from the water to press jump so that you have enough height to make it up without fluttering. Continuing holding B after you land and buffering a flutter off the ledge makes it easier to set up the next trick.
Green pirahnas normally require 3 shots to be killed, but they can be safely passed through for a brief period after being hit. Exploit this to get past the green pirahna at the end of the level with only one egg (or by spitting a nipper into him).
A safe method of getting the quick kill "Oh my!" on the boss is to go all the way into the boss room and stand on the edge of the ledge. As long as you do not go too far in, the boss fight won't trigger.