The boss fight can be skipped entirely by getting pushed into the staircase loading zone behind the center of the north wall. To do so, face the center of the north wall and use Link's shadow and the lines on the floor as a visual to align yourself correctly (north-south position is the one that matters). When Knucklemaster is done preparing his charge attack, he will back away from Link. At that moment, use the Tornado Rod. If done correctly, you will hear the sound of Link going up the staircase. Here are a video of the trick and a visual for Link's shadow.
Depending on your distance from the wall when doing the trick, you might have to hold up on the stick after using the Tornado Rod. If you are at a certain distance where the trick works without having to hold up, then it will not matter if you hold up or not, because it will work either way. Knowing that, it can be safer to always hold up after using the Tornado Rod.
The easiest way to position Link correctly for the skip is to get as close as possible to the north wall while facing it and do a single sword slash. This will push Link away from the wall and put him directly at the correct distance to do the skip. Just know that this particular distance requires you to hold up after using the Tornado Rod. If you move Link down a little bit more after slashing the wall, then you will get in the range where holding up isn't required.
The best way to fight Knucklemaster is to always stay close to the north wall of the arena, because it provides a rather large area of unbreakable floor (as seen in the picture below). For the first phase, you want to simply merge the north wall when he starts charging his fist attack, unmerge as soon as he hits the wall and hit him as many time as you can with your sword. For the second phase, dodge his slap attacks by moving left and right over the unbreakable floor. Repeat the first phase's strategy when he starts charging his fist attack again. A few cycles of the second phase and Knucklemaster will go down.
When you enter the room, step on the switch and keep walking to get on the rising platform in the center of the room. Throw 2 bombs to either of the top Gidbos, jump down and go merge the wall under the other one to have the Wallmaster take care of him. Finally, use your sword to deal with the remaining Gibdo and Mini-Moldorms.
After dropping down into the room on floor B1 with the south most exit, step onto the platform and merge into the nearby wall. If you travel along the wall in the opposite direction that the platforms are circling around it, you can un-merge onto a platform that will take you directly to the ledge with the key chest.
In the first room of B2, there is a puzzle where the objective is to push two statues onto a set of switches in order to create a wall that can be merged on to reach the next room. You can skip pushing one of the statues by pushing one of them onto the rightmost switch, then using the Tornado Rod to get on top of the wall as it's moving in place.
In the room before the miniboss, it is possible to dash from the top of the stairs directly to the central area. The Dash-Cancel Momentum technique isn't required, a simple dash will be enough to reach it.
In the north-eastern room on floor B2 there is a set of moving platforms, and a key underneath a mesh platform. Normally to reach this key you would have to ride in underneath the left platform, which moves really slow. However, you can use the Pegasus Boots dash cancel trick go from the ledge with the door to the ledge with the key chest. Once you obtain the key, you can simply return to the platform next to the locked door by falling out of bounds, as the game will not count you as standing on safe ground while standing underneath the mesh platform.
The best way to transport the eyes within this room is to use the hookshot to pull them toward you, rather than head out toward them. The eye in the top-right corner is easy enough to get to: just Hookshot it and throw it into place. The second eye is a little trickier. Head for the exit at the south end of the room, and re-enter the dungeon from the flower patch just to the north-east. Once inside again, merge into the wall to the east, and head north until you can stand on solid ground, then head back to the wall with the Master Ore chest on it. From here you should be able to longshot onto the eye. Head back to the wall you came from, and jump down from the platform with the eye on the east side and make your way back to the Boss Key chest.