An essay on The Old Man and the Sea could cover any number of topics, from Hemingway's use of language to the themes of religion and determination. For example, you could take the character of Santiago, the old man, and examine his internal monologue throughout the book, seeing how it changes from confident and serene at the start to almost scared near the end. Santiago goes through a great ordeal and so his confidence slowly wanes.
Another good topic is the relationship between Manolin and Santiago. Manolin is a young boy who wants to learn from Santiago, even though his parents think Santiago has become unlucky, and shows him devotion and honor throughout the story. His youthful exuberance at the beginning could be contrasted with his more adult reaction at the end, when he takes practical steps to help Santiago recover. Even though he doesn't appear in the main events of the story, his personal growth is obvious by the end.
For more information and ideas on what to write, read the eNotes study guides linked below.