Is Pi a hero by the end of the book Life of Pi?

It depends what you mean by hero. Over the course of the story, Pi does do some incredible things including saving his own life, escaping peril, and caring for the tiger that resides on the boat with him. He is regarded as miraculous and impressive, and his story is very incredible, but he doesn’t necessarily reach hero status.
By nature of being the protagonist, he is the “hero” of his own story, but because his actions were not necessarily heroic, it is hard to deem him a hero. For instance, he is not seen fighting for a cause other than survival, and he doesn’t show incredible strength or leadership, which are some archetypical traits of a hero.
Instead, because his story becomes widely publicized and people are very interested in hearing about him, he reaches more of a legendary status than a heroic one.