Your question touches at the heart of the novel and it is very interesting to study the function of the beast and how the different characters react towards it.
The beast is an imaginary creation that represents the savage, primal instinct that exists within all humanity. It is noteworthy that as the boys indulge in more acts of savagery and decline further morally, their belief in the beast grows accordingly. By the end of the novel the beast is being sacrificed to and it is almost a god that they worship.
The figure of the beast is of course inextricably linked with the Lord of the Flies: the sow's head that Jack impales and leaves as an offering to the beast. The sow's head seems to become a physical manifestation of the beast when Simon enters the glade and "talks" to him. It is only Simon who has the courage to face the beast and to discover the truth - that the beast is the evil that lurks in all of them. When the Lord of the Flies promises to have some "fun" with Simon, we see Simon's death foreshadowed and it strengthens our feeling that the Lord of the Flies represents the force of evil in this novel - if Simon represents Christ, then the Lord of the Flies represents Satan.
Based on this central idea then, you will want to examine how each of the characters "relates" to this theme of savagery. Jack and Roger of course allegorically represent the forces of savagery. From the beginning they delight in pig-hunting and the abuse of power. Ralph is a more complex character because although he represents civilisation, he still feels the attraction of savagery, joining in the pighunt and also the wild dance and Simon's death. Simon of course is the force of goodness in the novel who realises the truth and alone has the courage to face the Lord of the Flies. It is then that the Lord of the Flies confirms what Simon had suspected:
There isn't anyone to help you. Only me. And I'm the Beast... Fancy thinking the Beast was something you could hunt and kill!... You knew, didn't you? I'm part of you? Close, close, close! I'm the reason why it's no go? Why things are the way they are?
Hope that helps! With this basis you should be able to flesh out the rest of your essay.