Night Tide (1961)

While on shore leave, sailor Johnny Drake (Dennis Hopper) becomes enamored of Mora (Linda Lawson), a young woman who works as a "mermaid" at a sideshow attraction. But for Mora it's no act. She actually believes that she really is a mermaid who is destined to murder men on the night of a full moon. Drake is still captivated by the mysterious woman, however, and begins to suspect that her boss, Capt. Murdock (Gavin Muir), may have something to do with Mora's murderous thoughts.