How does the statement below apply to Hamlet and Life of Pi: This above all: to thine own self be true, and it must follow, as the night the day, thou canst not then be false to any man.

The line quoted is spoken by Polonius in Hamlet as part of the advice he gives to his son, Laertes, who is leaving home. The irony of the speech, especially this line, is that Polonius does not uphold the principles he recommends to his son. Laertes returns home late in the play to find both his father and his sister dead; Hamlet has killed Polonius. Laertes does behave according to these principles: he challenges Hamlet to a duel to avenge Polonius's death.
The entire play centers around Hamlet's efforts to be true to himself as he simultaneously tries to avenge his father's death and behave as an ethical person. He does not totally succeed. To accomplish his goal of revenge, he pretends to be mentally ill and thus deceives everyone around him. He hesitates to kill Claudius at prayer—a moral decision but one that blocks him from achieving revenge. Finally, at the end, he does achieve Claudius's death but only by sacrificing himself.
In Life of Pi, Pi struggles to stay alive in the boat by outwitting the other characters. Unlike Hamlet, who feigns mental illness, Pi seems to be living in a fantasy world. He engages with fellow passengers that are animals, including the tiger Richard Parker that Pi must keep away from him.
In the end, Pi reaches safety and tells this story to the investigators; predictably, they do not believe him. Pi then offers a more logical explanation. Pi did stay true to himself in the sense of achieving his goal of reaching safety, and like Hamlet he paid the price for causing other people's deaths; unlike Hamlet, however, Pi survived.