The originally setup for Aeralfos Skip is not viable in TPHD cause the lack of notches on the control stick makes moving straight up and down hard.
The alternative setup for TPHD is still hard cause of gyro controls and the difficulty of a 180° turn.
Hold L during the cutscene, skip the cutscene and Jump attack out of the cutscene.
Now slash 3 times, but don't finish a full combo. Turn around and find the pixel. Staying on the pixel with gyro aiming is very hard.
Start by hitting the Aeralfos with the Boomerang to make it pull out his shield, then use the Clawshot to pull him down to the ground. Take out the Ball & Chain, swing it into him five times. Aeralfos should block the last attack. Immediately use the B&C again until he hits you, the attacks will be visually blocked by his shield but still damage him. After standing up make a step towards Aeralfos, hit him with the B&C once and then throw it so it finishes Aeralfos off on return.
Start by hitting the Aeralfos with either the Bow & Arrow or Boomerang to make it pull out his shield, then use the Clawshot to pull him down to the ground. Take out the Ball & Chain, swing it into him four times, and release it on the fifth swing. The Aeralfos should block the last attack and counter it, however when the ball returns it will hit him one last time. For it's second phase, grab him towards you with the Clawshot and swing the Ball & Chain like before to defeat him.
For other Aeralfos fights in the game (such as in Hyrule Castle), they only use the first phase of this fight.