To avoid having to defeat the enemies in the room, the standard strategy uses a damage boost off of the right-hand Popo to gain invincibility frames, allowing you to pick up the pot and trigger the switch as your invincibility wears off. Diagonal wiggling / stair pumping should then be used to climb the stairs faster.
Care must be taken to navigate around the Popo -- the damage boost can usually be triggered efficiently using an up-left input. The Anti-Fairies will ideally knock you diagonally upward, but this can vary depending on both your position and timing and must be reacted to.
Regardless of armor, the hit from the Popo deals half a heart of damage and the hit from the Anti-Fairies deals an additional heart of damage.
If your initial invincibility frames wear off before you are in position to hit the switch, you can opt to try again, using either a Popo (if one is still nearby) or the Anti-Fairies themselves, but keep in mind that each extra attempt will cost additional health.
The four antifairies in this room cannot be powdered into fairies. This applies even after they are "released" by defeating the rest of the enemies in the room.
An optimal capedash saves 14 frames over walking and pausing to activate the cape, and only uses 18 magic compared to 12 - a net gain of 8 frames even when accounting for cutscene magic refill time. The capedash is also arguably easier to execute optimally.
Together with a "poof walk", the capedash can theoretically be around 11 frames faster than the damage boost strat, though this time is usually more than negated by the extra magic usage, making the choice of strategy largely up to personal preference and resource management.
Using the hookshot can save time when climbing the stairs, either through diagonal movement combined with a hookspeed setup (usually easier), or by simply hookshotting to the chest about halfway up.
Since the big key door is closer to the left, walking around the left side of the raised platform is faster, unless the Popo is in the way and needs to be slashed, in which case going around on the right is faster.
After opening the chest, a hookspeed or spinspeed setup can be used to reach the door more quickly. As mentioned above, the left path is usually preferred, but taking the right path is advisable if the left Popo is anywhere in the way, as maneuvering around it can be extremely tricky while in superspeed state.
If swordless (or not going for the spinspeed setup), the fastest way to the door is to dash upward, then walk horizontally to the door.
If the damage boost is not an option and no weapons are available, the enemies in the room can still be defeated (albeit slowly) by using the two pots, which respawn upon exiting and re-entering the screen.