i found that it is possible to make the fastest egg shot in 1-1 using princess. in order to do it, a slightly different clip must be performed in the cave.

the clip is tricky, but i will try to explain my best how to do it:

• first, you need to try to charge jump as soon as possible.
• once you are up top and grab the shyguy, throw him against the left wall.
• when you are at the bottom of the pit, press up as soon as the shyguy falls on your head, then immediately start holding down.
• once you are able to move again after taking damage, start mashing the down button.
• you do not need to be perfect, but the window in order to make the egg shot is pretty tight.