Palace of Winds

Palace of Winds has gone through big changes in the past year. It used to be completely glitchless until mid-2016, when we finally found a way to skip the Moblin Fight.
However, late April 2017 is when the big stuff happened. Thanks to the discovery of Boss Door Clipping, we are now able to skip the 2nd half of Palace of Winds as well as the Power Bracelets.
Despite the big skips, Palace of Winds is still one of the more difficult parts execution-wise. The first two screens can be quite frustrating due to Peahat RNG, and the Wizzrobe Fight is considered one of the more difficult strats.
The boss fight isn't very RNG-heavy, but can still lose you a lot of time if Gyorg gives you bad attack patterns.

Wizzrobe Fight

There are 2 main strategies for the Wizzrobe fight, one uses the Sword+Bombs and the other uses the Lantern+Bombs. Both are equally as fast, so use what you find easier.

Sword+Bombs

Lantern+Bombs

Cloud Jump Shortcuts

You can skip jumping up all the clouds by jumping up towards the top of the screen from different heights.
For most Cloud Jumps, jumping off the 3rd cloud will get you to the loading zone. For the Cloud Jump before the Ball & Chain Soldiers fight, jumping off the 2nd cloud is enough.

Power Bracelets Skip

Discovered by Yadra121

Using Cutscene Ocarina Glitch, it is possible to skip the Power Bracelets by skipping the Pot Puzzle. This skip would save about 90 seconds, while failing it wastes about 100 seconds.
Since you have to skip the Power Bracelets earlier in the run, you will not be able to progress through the dungeon until you eventually get Cutscene Ocarina Glitch successfully.
Due to the inconsistency and the fact that you only have one try to activate the Cutscene Ocarina Glitch, this is currently not used in Any%.

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Roc's Cape Shortcut

After acquiring Roc's Cape and jumping up the clouds to the next floor. You can make a precise jump over to the moving platform at the bottom left of the room. Skipping most of the floor and saving roughly 40 seconds.

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Moblin Fight Skip

Discovered by ToadsWoot

It is possible to use Cutscene Ocarina Glitch after defeating the Ball & Chain Soldiers, which allows you to skip the Moblin Fight as well as a few screens, saving about 33 seconds.
You only have one try, as the cutscene will be gone once you're too late.

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Skipping the 2nd Half of PoW

Discovered by ToadsWoot

Thanks to Boss Door Clipping, the 2nd half of Palace of Winds can be skipped completely, allowing us to directly go to the boss after obtaining the Boss Key.

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Gyorg Pair Strategy

You do not have to mimic Red Gyorg's eyes to hit all of them, it is possible to hit him with most formations. The .' . and . '. formations seem to work best.
It's possible to hit Red Gyorg's eyes across 2 cycles with the same pair of clones.
Only the 3rd phase actually has RNG in it, as the Blue Gyorg is flying around randomly and shooting things at you from all angles. Try your best to dodge them in order to not have to get new clones.
It is also possible to hit the .'' and ''. formations without using any clones. The .' . and . '. eye formations cannot be done cloneless.
To do this, you need to stand in rougly these positions and slash your sword once:

OUTDATED

Video Guide