Choose a theme for your biographical essay. While the obvious emphasis will be on academics and your chosen field, you will have more success in impressing the recipients if your biography has more of a focus. Resist the temptation to write your life story. Instead, choose one thread that runs through your life and base your narrative on that thread. For example, a pianist wishing to pursue a grad degree in music would obviously write about her lifelong progress on the piano, but a more focused theme would be her stage fright as a young student and how she struggled with and gradually overcame that fear of public performance throughout her years of study.
Write an outline for your biography. The outline should include an introduction and conclusion, as well as several main points for paragraphs in the body. Be sure each part of the outline, including the introduction and conclusion, touch on your theme. In the previous example, the pianist could break the body into different views of her stage fright: her first recital experience (or disaster), her avoidance of public performances, or her battle with choosing music as an undergraduate degree due to her fear.
Write a rough draft based on your outline. Allow yourself to write uncensored, as you will be editing and revising later, but focus on using words and phrases that will make the reader feel your emotion, rather than a dry narrative of facts and events. The biography should be in first person, but avoid using "I" in every sentence.
Take a break for a day or two from your biography, then read through it, aloud, if possible. Correct any spelling, grammar errors or awkward sentences. Read through it again and cut out any unnecessary sentences, and note any points that need further elaboration. Have someone read your biography when you feel it is strong enough to receive feedback. Revise it as many times as necessary until you feel the biography is ready.