By hitting Gyorg before dropping into the main room, you can skip the intro cutscene of the fight.
Use bow extension to shoot Gyorg from the spot shown in the video. This method is slightly slower than the weirdshot method optimally, and it also makes it harder (though not impossible) to hit Gyorg with the Zora barrier before the arrow stun wears off.
By damaging Gyorg next to the center platform, you are able to stunlock the first phase by swimming (with zora barrier) between Gyorg and the wall. The same carries into the 2nd phase, however now there are fish enemies swimming in the water as well. To stun Gyorg at the beginning of phase 2, you can use Zora boomerangs, a pot, the bow, or the hookshot.
Hit Gyorg with the Zora barrier once so that one Deku Sword jumpslash will kill it. Then stun Gyorg near the platform, jumpslash into hops on the water to get ISG, and drown above Gyorg to finish the fight, skipping the mid-fight cutscene. For a method that doesn't get ISG, see the video below.
Using Fierce Deity, you are able to damage Gyorg from that platform with sword beam stabs. This is useful for SRM categories that have Fierce Deity early.
Standard methods for remains escape after defeating Gyorg are slow when you have lots of health because the best way to leave the dungeon is to void as Goron, play Song of Soaring to get to the entrance, and then leave via the turtle. This method lets you soar to your next destination right after voiding, which saves significant time if your next destination isn't Zora Cape.
Voiding late will mean you have to watch the giant cutscene, though Link will be Goron during the cutscene. Voiding early brings Link back to the room's entrance, where you can soar out as though you had done standard remains escape and voided.