In the early 19th century, during the Napoleonic Wars, the British Royal Navy frigate HMS Surprise, captained by the experienced and relentless Captain Jack Aubrey, is on a mission to track down and capture the French privateer Acheron. The Acheron, a much more powerful warship, is intent on disrupting the British whaling fleet in the Pacific. As the film begins, the Surprise is suddenly attacked by the Acheron, which emerges from the morning fog. Despite the Surprise being heavily outgunned, Captain Aubrey executes a daring escape and begins a high-seas game of cat and mouse with the elusive French ship, driven by both duty and personal pride to pursue his adversary and bring her to battle.

Amidst the naval chase, the ship's surgeon, Dr. Stephen Maturin, who is also a naturalist and close friend to Aubrey, is torn between his duties to the wounded and his scientific curiosity about the Galapagos Islands' unique flora and fauna. The crew of the Surprise faces numerous challenges, including severe weather, dwindling supplies, and the toll of prolonged isolation at sea, which tests their resilience and camaraderie. As the two vessels draw closer, the strategic duel between the captains escalates, with Captain Aubrey's leadership skills and the loyalty of his crew being crucial to overcoming the formidable obstacles they face from both the enemy and the unforgiving maritime environment.