By getting into position and precisely clawshotting the target (aim at the little blue dot), it is possible to skip the Aeralfos fight, which saves around 40 seconds. Unfortunately, unlike the GameCube version of the game, HD does not have notches or angle buffering and does have gyro, so the trick is much harder. There are four ways of getting into position for the trick:
With the iron boots on and the sword out, jump attack once (mash out of the cutscene), do three neutral slashes, then turn around.
The following video contains data viewer information showing Link's position and angle.
With the iron boots off, do three neutral slashes and a fourth slash while holding forward, then turn around.
With the iron boots on, roll backwards once, then take off iron boots and roll forwards once. Without notches, this setup can be inconsistent.
With the iron boots off, roll forwards once, then put on the iron boots and roll backwards once (be sure not to rush this second roll or you will end up too far down). Without notches, this setup can be inconsistent.
Normally, after Aeralfos takes a certain amount of damage, the second phase of the fight will start. However, you can deal more damage without starting the second phase by hitting Aeralfos's shield during attacks (shielded hits when Aeralfos is standing there blocking do not count), and if you deal enough damage, whenever you land a real hit, Aeralfos will die, skipping the second phase. The damage thresholds are:
Ideally, the fight goes like this: Start by hitting the Aeralfos with the boomerang to make it pull out its shield, then use the clawshot to pull it down to the ground. Take out the ball and chain and swing it into him five times. Aeralfos should block the last attack. Walk forward slightly and swing the ball and chain around as Aeralfos tries to hit you (with a slow attack, you should get three hits). Stand up, walk forward slightly, hit Aeralfos with the B&C once during its attack, and throw the ball and chain. If successful, the ball and chain will hit and kill Aeralfos on the way back.
Sadly, Aeralfos's attacks are not entirely consistent. If it does a fast attack, you might only get one shielded hit, in which case you need to count up to four hits before hitting it with an unshielded ball and chain attack (or up to five hits before hitting it with a slash). In general, however, Aeralfos should never fly back up more than once before you are able to kill it.
Start by hitting Aeralfos with either the bow or boomerang to make it pull out its shield, then use the clawshot to pull it down to the ground. Take out the ball and chain, swing it into Aeralfos four times, and release it on the fifth swing. The ball and chain should hit and kill Aeralfos on the way back. Repeat the process for the second phase (Aeralfos should die on the fourth hit if you did the first phase correctly).
Other Aeralfos fights (for example, the one in Hyrule Castle) work exactly like the Quick Aeralfos Battle, except that there will not be a second phase.