When writing a biography, think of it as the story of a person's life. A good story has an exposition, rising action, climax, falling action, and finally a conclusion, and so should your biography!
The first part of the biography should contain the early life of the person you are writing about. This means their birth, family, education, etc. Your reader should also be able to figure out the character of the person you're writing about in this section, and, just like the exposition of a tall tale, this part should also contain information on your subject's inspiration for their accomplishments.
The second part of the biography (the rising action in our example) should contain information on how your subject got to their climax (the most important thing they did). This includes what they did before getting to the climax, and how they eventually got there.
The third part of our biography is the subject achieving their dream or doing what they will be remembered for. A good example would be JFK finally becoming President, or JRR Tolkien writing The Lord of the Rings.
The falling action should contain what your subject did after their climax, eventually leading to the conclusion, their death.