How is life of Pi an allegory about fear?

I think it is possible to read Life of Pi as an "allegory of fear," so long as we take into consideration the multitude of things going on in Yann Martel's stunning novel. 
It is true that fear is working its way into Pi's mind as he attempts to process the strange world around him. He presumably has great fear for his mother as he watches her meet her end on the raft. And soon, he inherits the sum total of what fear remains, as he wonders whether or not he will survive. I think another important topic in Martel's work is trauma, and the curious way that the human brain works when it is subjected to intense duress. 
In the novel, Pi conjures up a world that might be fabricated purely from trauma. But his ultimate thesis is that the "fabricated" world may not be any less real than the "real" one. A boy alone on a raft exists only in the reality his mind creates; this is the fundamental teaching of phenomenology. 
And in this fantasy world, we come across a third fear that is more abstract; the fear he has for Richard Parker, which ultimately, is the fear he has of himself. And so our "Man vs. Wild" narrative gets curiously intermingled with a "Man vs. Self" story line, where the wild is the self, and proves just as terrifying in either format. 
Yes, fear is a central theme to Martel, taking its place alongside trauma, spirituality, imagination, and grief. 

One of the key themes in Life of Pi is the idea that life is a story. Fiction is quoted as being the "selective transforming of reality". We can apply this notion to Pi's trauma in the course of the novel and thus explore how Life of Pi is an allegory of fear. The bulk of the novel tells the tale of Pi, stranded on a lifeboat with a tiger, hyena, zebra and orangutan. As Pi is the first person narrator, the reader sees this account only through his eyes. However, in Part 3, Pi is rescued and interviewed by two investigators, to whom he tells a very different version of the story with human characters instead of animals. Parallels are drawn between his mother and the orangutan, the hyena and a cannibalistic French cook, and the zebra and a wounded sailor. Pi's mother and the sailor are devoured by the cook. Pi himself ultimately devours the cook. 
The latter version of the story is clearly the more believable but also the more unbearable. Pi challenges the investigators to say which is the better story. Pi uses the allegory of the shipwrecked animals in order to deal with his trauma and experience of fear. The same can be said for his devotion to religion - Pi posits that a life with religion is the better story, whether it is true or not. This is how Life of Pi can be read as an allegory of fear.