With a sword and no boots, you will need to react to the RNG patterns of the lower two Stalfos enemies and dodge or slash accordingly if one or both of them are in your way. The above videos show a possible set of reactions for the different cases.

With boots and a sword, you can walk south and charge a dash before fully clearing the rectangular rail (nudging off of it during the dash). Doing so will ensure that you can charge the dash safely even if the first Stalfos decides to move all the way to the right.

If you only have a fighter sword, the second Stalfos will have to be avoided if it stops its movement halfway instead of continuing to walk to the right. You can try to take a step upward or downward to avoid it, or opt for a slightly slower (but safer) walk to the door.

Link will not make any progress toward pushing the block while a diagonal input is held, so it's important to make sure that you are holding straight up when you reach the block.

Pressing up-left after the block movement initiates will cause Link to remain in a "block-pushing" animation as long as up-left is held. Although Link may appear to be stepping more slowly during this animation, the actual rate of movement is exactly the same. Of course, optimal movement will air/wallpump rightward while facing up, but the point is that buffering the leftward movement around the block won't result in any lost frames.

After dashing up, it's fastest to dash right through the door rather than walking.