The Megalodon shark (Carcharodon megalodon) is certainly a good candidate for such a movie. It is far from mythical, however. These terrifyingly-impressive 40-50 foot long versions of the White Shark did in fact once lurk in the waters of the distant past.
It is believed that these very real monsters became extinct sometime in the mid-to late Pliocene era. That is probably a good thing. Otherwise I doubt many people would care to risk a salt-water swim.
The possibility that the Megalodon survives is unlikely, but not altogether impossible. For centuries, people have told of sea serpents and monsters of the deep. Most are probably little more than the overactive imaginations of seamen mixed with too much alcohol. Some, however- such as the giant squid, once thought to be a myth- have been confirmed as real, living animals.
Then something happened in 1977 that caused a sensation. A Japanese fishing vessel trawling for mackerel hauled up an unidentified carcass of a huge creature weighing in at 4,000 pounds. The carcass was badly decomposed and smelled horrible, so they eventually threw it back to avoid contamination of their catch. But before they did, pictures and tissue samples were taken of the creature.
The photos clearly show, despite the decomposition, an animal with a long neck, small head, smooth back, and large, paddle-like flippers. While it's never been confirmed, the body pulled aboard certainly looks like it may be a plesiosaur-like animal.