According to the Örvar-Odds Saga, the Hafgua was the mother of all sea monsters. This giant monster fed on whales, ships, men, and anything it could catch. It inhabited the Greenland Sea and may disguise itself as a pair of rocks rising from the sea. Those two rocks are its jaws, its nose and lower jaw.
The Hafgua lived underwater, but it was so big that when the tide was low her nose and head would rise out of the water, looking like a rocky island.
The only physical description know of this creature is provided by the Örvar-Odds Saga indicating that the Hafgua’s nose sticking out of the water was mistaken for two massive rocks rising from the sea.
When legendary hero Örvar-Oddr (see note below) and his crew were sailing through the Greenland Sea—a very dangerous area—they spotted two rocks that rose out of the water. The presence of these rocks puzzled Oddr. Soon after, they passed by a large island covered in heather. Inquisitive, Oddr decided to turn back and send five men to check out the island, but as they approached the point where the island had been before, they saw that it and the two rocks vanished.
Vignir, the deck officer, explained to Oddr that if they had actually landed on the island, the crew would have surely drowned for the "rocks" and "island" must have been two sea monsters—the great whale Lyngbakur, and Hafgua. The rocks had surely been the nose of Hafgua; the island, Lyngbakur.
Some scholars believe that references to the Hafgua are reference to the kraken. However, others believed that there are two different monsters.
Note: In Old Norse the name Örvar-Oddr, can be translated as "Arrow-Odd" or "Arrow's Point"
-Boer, R. C. (1888). Örvar-Odds saga. Leiden: E. J. Brill. p. 132.