Frog Airswim
Frog Airswim is a glitch that allows Mario to swim through the air as a frog to reach an indefinite horizontal distance. This is most notably used to skip the entirety of the Darker Side dungeon, where it is often known as Frog Skip.
This glitch is only possible on version 1.0.0, so it is no longer optimal for Darker Side speedruns due to version 1.3.0 having the fastest load times by a significant margin. However, it is useful for Darker Side Minimum Captures, since it can allow the kingdom to be completed in a single capture.
Methods
Midair capture method
One way to reproduce Frog Airswim is by capturing a frog just after bouncing on it in midair. The frog must be somewhat high in the course of its jump, so the easiest method to gain height before attempting it is to capture the other frog, jump and then uncapture it; however, it can also be done simply by jumping high enough, such as using a backflip[1]. This must be timed so that Mario lands on top of the frog that will be used for the glitch while it is jumping upwards. Pressing X or Y to throw Cappy just after landing on the frog will cause it to immediately be captured, and it will enter the swimming animation, stalling it in midair.
Dorrie method
Frog Airswim can also be triggered by swimming in the pond onto Dorrie's back in a specific way. First, the player should swim right up to the edge of Dorrie's back, but not close enough that the frog exits the swimming animation. Every time Dorrie bobs downward, the player should swim slightly more onto his back. If done correctly, the frog will remain in the swimming animation while slowly climbing higher out of the water. Eventually, the frog will be high enough to swim over the edge of the pond and all the way to the end of the kingdom.