If skipping the chest in this room and proceeding onward, starting a dash from the doorway without moving is optimal as it will allow you to perform a keydash through the door to the next room.
The easiest way to avoid the bunny beam is to stand still in the doorway and wait for it to disappear (as it cannot enter the doorway). You'll want to walk out of the doorway immediately afterwards in order to avoid the wallmaster.
Note that this strategy only works in the left doorway -- the bunny beam is able to reach Link when he is in the right-hand doorway.
The interval at which the wallmaster appears is consistent and is not affected by hitting or killing it -- it will always reappear at the same fixed interval.
It is, possible, for some wallmaster spawns to be "skipped" if there are too many sprites on the screen at once. This is commonly seen if the two shooters in the room are repeatedly triggered, but having other sprites on screen (e.g. bottled bees) can also contribute. Unfortunately, there is no known practical setup for easily preventing 100% of the wallmaster spawns.
The chest in the top of the room only appears after all 22 flying tiles have spawned (which takes around 35-40 seconds). However, the chest also won't spawn if the wallmaster is on screen. Both the tile and wallmaster timings are fixed, and line up so that if you allow the final tile to fly toward link and disappear by hitting a wall, you'll have to wait for another wallmaster cycle before the chest appears.
You can eliminate this delay altogether and save over 3.5 seconds by making the final tile disappear sooner -- either by being struck by it earlier, or (preferably) by hitting it with a weapon after it becomes active. Some simple ways to do this are to simply hold your sword out (keep in mind the position of the two shooters in the room), or to use a somaria block.
Since there are multiple obstacles in this room to avoid simultaneously (the flying tiles, the anti-fairy, and the wallmaster), a simple and common way to safely wait out the tiles is to take advantage of Magic Cape Cheapskate by grabbing onto a wall to minimize magic drain.
The bunny beam will continue to track Link while using the cape and won't despawn after any amount of time. While it's technically possible to outrun the bunny beam afterward using cardinal movements or dashes, this is risky and consumes additional magic, so you'll want to despawn the bunny beam before activating the cape, using the doorway strategy mentioned above.
This doorway spin slash strategy takes advantage of the fact that the only obstacle in the room that can hit Link from the initial position in the doorway is the wallmaster. Enter the doorway with your sword held out to the left, up, or down -- holding your sword to the right will not work as it will result in poking the tiles (and dropping your sword). From there the only thing you need to do is time spin slashes to kill the wallmaster every time it spawns. There will most likely be a reduced number of wallmaster spawns because the shooters will constantly be firing, causing some spawns to be skipped (as described earlier).
This can be done with any level sword, but the timing is slightly more strict with fighter sword, since your spin will need to hit twice in order to defeat the wallmaster and avoid being grabbed. In this case you should wait until just before the wallmaster grabs you to release your spin slash, as shown in the above video.