Compare The Life of Pi to the Hero's Journey.
Different scholars on literature and mythology have different steps and stages in the hero's journey, so this can be done a few different ways. I will use Joseph Campbell's hero's journey to review Pi's tale.
The Ordinary World: Like the exposition in a story, this is the part of the journey where the audience learns what the hero's everyday life is like before the adventure. Nearly everything that happens to Pi in India fits into this part of the journey.
Call to Action: This is the moment when the hero's life will change from what it once was. In Pi's case, this is when his father declares that they will be selling the zoo and moving to Canada.
Refusal of the Call: There isn't a big refusal in Pi's story, but he is reluctant to leave his life behind. In the hero's journey, the hero typically refuses to go until persuaded by an event or mentor.
Crossing the Threshold: In the hero's journey, this is the moment when he leaves the ordinary world to enter the special world, which has new rules and will test him in new ways. In Life of Pi, this is when Pi is ship-wreaked and finds himself on a raft, with his family dead.
Meeting the Mentor: The hero rarely goes through her trials alone, instead she often has an older and wiser mentor. In Pi's case, his mentors are the animals with him on the raft, particularly the tiger, with whom he forms an unlikely and spiritual bond with over time. His survival handbook also acts as a more practical mentor.
Tests, Allies, Enemies: The hero travels through several small obstacles and meets others who can help or hinder him. Pi is faced immediately with multiple tests from his environment. He also has the orangutan as an ally and the hyena as the most immediate enemy.
Approaching the Inmost Cave: This is when the hero prepares for her final test. In Pi's case, that test will be surviving with the tiger, and he works to train him using the boat and seasickness.
The Ordeal: This is where the hero confronts death in the special world and has to overcome something particularly terrifying. In Pi's case, this is when the thunderstorm hits, bringing flying fish and forcing him to hide with the tiger, furthering their bond.
The Reward: The reward is the treasure that the hero earns by overcoming the ordeal. In Pi's case, this is the island with the edible plants, fresh water, and meerkats. Here he can rest, recover, and prepare to make the final leg of his journey.
The Resurrection: This is the hero's final death and rebirth to prepare for the journey home. In Pi's case, he is tempted to stay on the island and renounce society, until...
The Road Back: This is when the hero is finally pushed to leave the special world. When Pi realizes that the island is carnivorous and they must leave, he begins the road back, which ends when he and the tiger land on the beach in Mexico.
Return with Elixir: This is the part of the hero's journey when the hero comes back home with some sort of power of treasure that he can carry with him. In Pi's case, this treasure is his faith and knowledge of the world that his experience has given him.