I need to approach an essay about "Annabel Lee" by Poe from either a biographical or an historical critical approach.
While the losses in Poe's life through the deaths of beautiful beloved women--his mother, his friend's idolized mother, his young wife--is reflected in his poetry--just as his years living in England under the sway of Gothic influences is reflected in his poetry--his intellectual aesthetic of poetry is also reflected in his poetry since it is through this aesthetic theory that he builds his poetry. An historical approach to discussing "Annabel Lee" might take the route of discussing Poe's historic influence on the theory and development of literature.
According to the Critical Survey of Poetry, Poe, who was one of the few early American poets to be famous while still living, influenced the Symbolist movement in poetry because of their admiration of his conceptualization of "ideal beauty," the musicality of his verse (which some critics derided), and his ability to create atmosphere in poetry. Renowned poets who have similarly attributed admiration and influence to Poe are Yeats, Baudelaire, Eliot, and Dante Rossetti, along with playwright George Bernard Shaw and composers Stravinsky and Debussy.
Other impacts Poe had on the historical development of literature were to devise and advocate a criticism for poetry and book reviewing that exposed bad poetry and writing by insisting that judgments must be made on a system of standards that identifies defects. Along with this, he was a pioneer in defining a poem as a purely aesthetic object that could be justified on purely aesthetic grounds regardless of thematic meaning or truthfulness, as was advocated by the "art for art's sake" movement.
In conjunction with these ideas, he advocated leaving the realms of truth and logic to works of prose, such as the novel or short story, because poetry, an aesthetic art form, was primarily occupied with producing an effect on the reader. "Annabel Lee" can be analyzed in terms of Poe's theory and aesthetics and in terms of the qualities that made his work such a widespread and strong influence of other writers and on whole movements.
If I were writing about "Annabel Lee," I would take a a biographical approach. That would require a little research on Poe's life, which I won't do for you; but I have included a link to an excellent enotes site on his life, below. We do know Poe suffered a tragic loss of a young lady he loved, and that incident is certainly connected to this. In the poem, there is a distant family to which Annabel belonged and the sea and all-night vigils at the grave site, to name a few plot moments. See how many of those things, how much of the poem, does fit the story of Poe's lost love. Those points of comparison and points of divergence are the key elements of your essay, it seems to me. Happy writing!