"This massive monster swims beneath the desert's sand. It spends most of its time submerged, but if it senses sound, it will breach the surface to feast on whatever it can grab. Running around carelessly can be dangerous if you suspect there may be one in the area."
This boss swims underneath the sand, and has extremely good hearing, so if you move quickly it will be alerted and begin to swim to you. The best thing to do here is to stand on land which isn't sand, such as a broken pillar or a rock. You can use its hearing to your advantage though, by standing on a rock and tossing out a Bomb in its direction. It should notice it, and begin swimming toward it. Once it reaches it, the Molduga will jump out of the sand, swallowing the bomb. At this point, you should detonate the bomb and the boss will fall to the ground, vulnerable to hits. Run up to it and use a powerful two-handed weapon such as a Royal Claymore to deal great damage. Repeating this a few times will eliminate it quickly. Three uses of Urbosa's Fury should kill it as well.
Upon death, the Molduga will explode spectacularly, and drop a large amount of items. These include an array of Fins and Guts, as well as two chests, which tend to contain powerful weapons such as a Royal Broadsword or a Royal Halberd.