Perhaps they want to take a look at Mauna Loa's eruption.

Cthulhu rises from R'lyeh and the American Version of Godzilla (one who fought Kong recently) does too. Sensing each other, they clash in the water or on land.

Who takes it? Cthulhu has been whacked by a boat and recovered. In an approved story by Frank Belknap Long, he got hit by an H-bomb and had to go back home to recover. Godzilla survived the Pacific H-bomb tests aimed at him.

How does it go? This a physical battle and Cthulhu can't cast spells or take over G's mind (if he could). Atomic breath is allowed.