Penguins inexplicably arrive in town, sparking the curiosity of Aoyama. He uncovers that these charming creatures follow a unique route dubbed the "Penguin Highway," which intriguingly leads into the nearby woods. When the school bully, Suzuki-kun, ties Aoyama up to a vending machine, Aoyama is miraculously rescued by a mysterious figure known as the Lady, who transforms a soda can into a penguin as she frees him.
At school, Aoyama encounters his classmates, Uchida-kun and Hamamoto-san, while they play with a penguin named Penta on the rooftop. During their adventure, they bring Penta on a train ride, where it unexpectedly falls sick, escapes from its cage, and astonishingly morphs back into a soda can. Seeking answers, Aoyama visits the cafe to engage in a chess match with the Lady, who confides in him about her sleeplessness stemming from reading about the Jabberwock. In an amusing turn of events during a power outage, she accidentally transforms chess pieces into bats, further hinting at her peculiar powers: she can change thrown objects into penguins in light and bats in darkness.
The following day, Hamamoto leads Aoyama and Uchida deep into the forest, where they discover a surreal floating sphere of water that she refers to as the "sea." Over the next few days, the trio enjoys their time around the sea, investigating its mysteries. However, the situation takes a turn when Uchida tosses a toy spaceship into the sphere, causing it to disappear into its depths. One day, as Suzuki bullies the group, he stumbles upon the magical sphere, and Hamamoto warns him to keep quiet about it.
News crews soon report the discovery of a new unidentified creature, leading Aoyama and Uchida to witness this creature devouring a penguin. The Lady then invites Aoyama to the coast, and they journey by train. However, during their departure, she becomes ill, and her sweat inadvertently liquifies the concrete into a nightmarish Jaberwock. After this encounter, Aoyama loses sight of her for some time.
Upon returning to school, Hamamoto and Uchida find that access to the forest has been restricted. Despite warnings, they venture in and discover Hamamoto's father conducting research, only for Suzuki to expose the location of the mystical sphere. A fierce storm begins as the sphere swells, and the next day, its ominous growth results in the mysterious disappearance of Hamamoto's father. Amid a school lockdown, Aoyama manages to escape in hopes of reuniting with the Lady.
Aoyama pieces together the mystery surrounding the sea, realizing that it serves as the energy source for both the penguins and the Lady. Yet, the penguins appear to be attempting to destroy it, as the sea uniquely alters space and distorts time. Aoyama concludes that the sea acts like a hole, a rift in reality, and the penguins strive to repair this torn world. However, the overproduction of penguins adversely affects the Lady's health, compelling her to manifest the Jaberwock, which subsequently attacks the penguins and enlarges the sphere, ultimately restoring her vitality.
Together, Aoyama and the Lady journey toward the forest, inspiring a surge of penguins that blast through to the sphere, propelling them into a dystopian future. In this bizarre world, they rescue Hamamoto's father and his colleagues. As the penguins rise up and obliterate the sphere, water floods into the real world.
Returning to the cafe for a heartfelt conversation, Aoyama and the Lady gradually witness the penguins disappearing one by one. When the final penguin vanishes, she embraces Aoyama before departing from the cafe. Outside, she slips away from view, prompting him to resolve not to shed tears, vowing that he will see her again and express his love for her. Later, Aoyama notices a cat playing near the cafe where the Lady once stood. Approaching the spot, he discovers the toy spaceship that had been consumed by the sphere.
