On the other hand, we can attempt to structure our essay according to the outline.
On the outline, you were given a template to follow, making comparisons between Odysseus and O Brother's Everett. Let me attempt to clarify some things before you delve head first into that outline...
1. Everett is supposed to be a representative of Odysseus. Period. This means, every single action that Everett commits is supposed to represent Odysseus as a character. Some of this works out; some of this doesn't compute. It is up to you to decide whether or not, as a personality, if Everett can stand up to the epic hero that is Odysseus.
2. Notice in the point above that I said we are comparing personalities. Of course, actions are part of this, but not every action in O Brother finds an equal in The Odyssey. So, as you are setting up your character analysis, ask yourself, "Would Odysseus make the same decisions that Everett made in O Brother? Why or why not?" If you can answer that question a few times, you can then decide whether or not to defend, challenge, or qualify.