The first Morthula encountered in an Any% run is protecting the Boomerang in Forbidden Woods.
Immediately target the Mothula and maneuver Link over to the barred entrance door. This is easily done by holding ZL, Up on the left control stick, and Down on the right control stick. Right after the Mothula is at the peak of it's hovering oscillation, use the Leaf to blow a wind gust and stun the enemy. The delay caused by Link's animation will make the gust stun the Mothula at the lowest level of it's oscillation cycle. From here maneuver Link to the other side of the Mothula, placing it between Link and the door. After it slowly falls for about three seconds do four separate stabs to take off the wings and ground it (separate the stabs enough so that Link doesn't do the stab combo). After the Mothula is grounded, it has eight health. Ideally you can do two quickspins with the Mothula now cornered in a wall with each quickspin hitting twice.
You'll encounter Mothulas later in any speedrun of TWWHD. In almost all of these cases, you'll already have the bow and ice arrows. For grounded Mothulas you can simply kill them with a single bow shot, and flying Mothulas can be quickly eliminated with a single ice arrow shot.