At the end of the Gerudo Sanctum, you find a giant, sand-dwelling mole known as Mogryph.
How to Defeat Mogryph
First Phase
Mogryph will pop up from the sand and swipe its claw twice, shooting two gusts of wind and sand in the direction it was facing. Dodge the sand, but stay far away from Mogryph, because it will roar, and if you're close to it, you will be stunned by the loud noise. The roar will also make piles of sand appear. You can blow away the sand to get hearts and energy.
Mogryph will go beneath the sand, then will move around the edge of the room under the sand, and then it will stop and charge up an attack. Then it will dash straight toward where you are standing. Stand behind a statue to make Mogryph crash into the statue. The statue will break, and Mogryph will be stuck upside-down in the sand. Switch to swordfighter form and hit Mogryph repeatedly until it goes back under the sand.
Try making a statue in the middle of the room to make it easier to hide from Mogryph's dash attacks.
Second Phase
Eventually, the room with fill partly with quicksand, with some solid sand platforms, and Mogryph will fly up on its wings. If you bought the Gerudo Sandals in Gerudo Town, you can equip them so you won't sink (but make sure to unequip your other equipment first). Mogryph will create some whirlwinds. They move slowly across the room, so just make sure not to be in their path.
Then Mogryph will fly higher up so you can only see its shadow. Its shadow will fly above where you are standing, then fly downward. When it goes into the sand, it will move to a random location and do a dash attack like before. When Mogryph swipes its claws, it will now do two rapid slashes, followed by a third one.
Stand on a solid sand platform and put a statue in the path of Mogryph when it is going to dash. Then hit it repeatedly as before.
Keep repeating this strategy until the battle is over.
After the Battle
There will be a cutscene. Tri's gauge will increase. If Tri reaches level 3, you will be able to create echoes at a distance if you hold Y to charge up, then release it to create the echo. You get 5 Might Crystals.
Take the Heart Container (or leave it there for more of a challenge), then go north and talk to Tri at the glowing spot. Say Yes if you're ready to exit the dungeon. There will be a cutscene. This completes the quest "A Rift in Gerudo Desert".
There is a ladder on the ledge north of the palace, so use echoes to reach it. Go to the right side of the second Platboom and jump on top of it to reach the upper ledge. Then go to the right and create a Platboom to crush the boxes below. Pick up anything that fell out, then jump on top of the Platboom that you created, and bind to the giant boulder. Then as you are going upward on the Platboom, walk into the niche in the wall to move the boulder to the right. Press ZR to release the boulder on the ledge, then go down below and go past where the boulder was. You will find a Piece of Heart.
If you repaired the Jabul Waters Rift, the next quest, Still Missing, will begin. If not, read The Path to Jabul Waters to find out how to continue.