The story unfolds in 1805, against the backdrop of the Napoleonic Wars. Captain Aubrey, portrayed by Russell Crowe, commands the HMS Surprise, a British man-of-war, which is tasked with pursuing the French privateer Acheron with orders to either destroy or capture her. Just as the action kicks off, midshipman Hollom, crucial to the crew, catches a glimpse of something ominous in the fog, prompting a call to battle stations. However, their initial anxiety proves justified when the Surprise comes under heavy fire from the Acheron, leading to significant damage, including the ruin of their rudder. With their cannons ineffective against the Acheron's hull, the crew cleverly maneuvers the Surprise into the fog to slip away from the enemy.
As the situation develops, Aubrey learns that the Acheron, built with advanced design features in America, is not only heavier but also faster than his own ship. This revelation concerns the senior officers, who regard the Acheron as a significant threat that could tip the scales in favor of Napoleon. Rather than retreat to safety, Aubrey decides to carry out necessary repairs while at sea, all while keeping up the chase. They engage in a fierce pursuit, but the Acheron ambushes them once more. Utilizing a clever strategy, they evade in the cover of night using a decoy.
On their journey southward, the Surprise navigates around Cape Horn under treacherous conditions, resulting in the topmast snapping and tragically tossing a well-liked crewman into the sea. With heavy hearts, they must leave him behind to preserve the integrity of the ship. Their next destination is the Galapagos Islands, where Aubrey anticipates the Acheron will target British whalers. Meanwhile, the ship's doctor, Maturin, played by Paul Bettany, eagerly hopes to study the exotic wildlife rumored to inhabit the islands. Aubrey, in a show of camaraderie, assures Maturin that he will have ample time to explore upon their arrival.
Upon reaching the Galapagos, they rescue survivors from the whaling ship Albatross, which had fallen prey to the Acheron. However, the urgency to capture the privateer overtakes their plans, creating tension between Aubrey and Maturin, who begins to feel that pride is guiding Aubrey's decisions rather than duty. The Surprise soon finds itself becalmed, leading the crew to suspect they have a Jonah aboard, someone who brings misfortune. Hollom becomes the primary target of these accusations, facing scorn from his fellow sailors that culminates in a tragic outcome when he takes his own life by leaping overboard.
After mourning for Hollom, their luck seemingly changes as wind returns, allowing them to resume their pursuit. A dramatic incident occurs when a Marine, attempting to shoot an albatross, accidentally injures Maturin, necessitating urgent medical intervention. Despite being so close to the Acheron, Aubrey prioritizes Maturin's health over the mission and takes him back to the Galapagos for proper treatment. Maturin, showing his resilience, manages to perform self-surgery to remove the bullet.
Reluctantly acknowledging the necessity to prioritize his friend's welfare, Aubrey grants Maturin time to explore the island. While searching for a rare species of cormorant, Maturin unexpectedly finds the Acheron. He hurriedly informs Aubrey, prompting the crew to prepare for combat. Given the formidable Acheron, Aubrey cleverly devises a plan to disguise the Surprise as a whaler to lure the French crew closer, capitalizing on their greed. The tactic works, and as the Acheron approaches, the Surprise spring into action, successfully undermining the enemy's defenses.
In the ensuing board battle, Aubrey, alongside his loyal officer Pullings, directs the charge against the Acheron, aided by whalers who had previously been imprisoned aboard the French ship. After subduing the enemy, Aubrey learns that the French captain has met his fate, and the ship's doctor offers him the captain's sword as a sign of respect and defeat.
Amidst repairs, the Acheron prepares to sail away, and Pullings receives a promotion to Captain, assigned with the task of guiding the captured vessel to Valparaiso. However, a twist awaits as Maturin uncovers that their adversary tricked them, disguised as the dead doctor. With a mix of surprise and determination, Aubrey once again calls for action, setting a course after the Acheron, much to Maturin's dismay, who is denied another chance to explore the Galapagos. In a moment of shared levity, Aubrey muses about the flightless bird Maturin seeks, saying, > "It's not going anywhere." They begin to play music together on their instruments as the crew readies for yet another intense naval engagement.
