To begin the fight quickly, press B to pull the sword as soon as possible after entering the room and jump attack from where Link is standing, then skip the cutscene. Transform into wolf, turn on senses, approach Death Sword, wait until it swings its sword, and then finish the first phase of the fight by biting repeatedly with A or with five timed B attacks (the B attacks are slightly faster). To prevent the B attacks from missing Death Sword, space them so that the last 3 are part of a separate combo from the first 2. Note that it is possible to softlock by bonking into Death Sword's sword on the final B attack.
The following is a video example of the B attack method.
With a precise wolf super jump, it is possible to skip the second phase of the Death Sword fight. This saves about 16 seconds over the one-cycle.
Skipping the slash in the setup described above saves about three seconds at the cost of having less time to get into position after transforming.
If Death Sword gets stuck flying in place after circling the room, it is still possible to get it into the correct position for the super jump.
Alternatively, if you aren't comfortable with the backup described above, you can hit Death Sword to get it to spin around the room again. The quickest way to do this is to target it, hit it with the clawshot, press B to pull out your sword (to delay the timing a bit), and then hit it with the clawshot again. Unfortunately, this does not guarantee that Death Sword will spin the correct way the second time.
Death Sword's stun timer begins when it is hit for the first time, but the third part of a sword combo will reset its timer. Repeatedly resetting the timer makes it possible to finish the fight in one cycle. Note that the first and second slashes of a combo do not reset the timer, and finishing a 4-part combo will always end the timer.
Hit Death Sword with the clawshot or boomerang to make it fly around the room, then charge a spin attack. Release the spin attack when Death Sword is flying by to knock it to the ground. Swing the ball and chain to hit Death Sword three times, then hit it with three three-slash combos (do not finish any of these combos) followed by a full four-slash combo.
It is faster to hit Death Sword four or five times with the ball and chain before doing the sword combos, but this makes it harder to reset the timer with the first three-slash combo before the timer runs out.
The following is a video example of the three-hit ball and chain method.
Hit Death Sword with the clawshot or boomerang to make it fly around the room, then charge a spin attack. Release the spin attack when Death Sword is flying by to knock it to the ground. Hit Death Sword with a jump attack, then five three-slash combos (do not finish any of these combos) followed by a full four-slash combo. Alternatively, you can skip the jump attack and just do seven three-slash combos. To avoid doing a four-slash combo, wait until the sword starts coming back up after the third slash before starting a new combo.
This method is around three seconds slower than the three-hit ball and chain method.
Death Sword has two conditions which cause it to fly away after being knocked to the ground and only one of them has to be true for it to fly away:
The one-cycle strategy abuses the fact that the timer doesn't run as long as you are slashing your sword (even if you aren't actually hitting Death Sword).