Sea monster

Psalm 74:13-14 - It was you who split open the sea by your power;
you broke the heads of the monster in the waters.

It was you who crushed the heads of Leviathan
and gave him as food to the creatures of the desert.

I wonder if this is a reference to Moses and Israel passing through the Red Sea. There was no mention of any multi-headed sea monster in Moses' account however.

If this is not a reference to Moses time, then I wonder when this did happen. And what is this sea creature that has more than one head? Leviathan is mentioned in other places in the Bible, but I don't think anyone knows exactly which creature the term describes. In Job 41, leviathan sounds like the dragon of fantasy literature. Why not a two-headed dragon then as well?