You can attack literary analysis of Hatchet from several different directions. For instance, you could write about character development and the way Brian Robeson's experiences alone in the wilderness change him in the story. How is he different at the beginning and at the end, and how does the change in him happen?
Alternatively, you could focus on nature itself. In the story, the wilderness is both Brian's tormentor and his teacher. Do you think Gary Paulsen romanticizes nature in the story?
A third option would be to examine the writing style. Brian is alone through most of the story. How does Gary Paulsen develop his character and show changes in Brian largely without using dialog and the reactions of other characters--two tools that are most often serious parts of characterization?
The above answer does a great job listing you some questions that are good themes that you could write on and use for literary analysis. However, I will help you by going more in depth on one of them: character development with Brian Robeson.
Throughout the book, we get witness into the survival of Brian and how his instincts and wit lead him to surviving the wilderness. When the initial plane crash hits and his pilot dies, readers are able to see that Brian is lost mentally as well as physically. He does not know what to do or how to act, as he is mainly in shock. This is clear as he attempts to go for the first aid and emergency pack that is located in the plane. However, by the end of the book, we see how naturally easy it is for Brian to go about his daily business in the wild. Kill a fish for dinner? Easy. Build a shelter and roof to stay warm throughout the night? No problem. Defend himself against dangerous animals? Why not. It is really quite amazing the type of progress he was able to make and the adjustment that he made in order to prosper through the grueling conditions. It makes for a great theme because true perseverance and committment is very present in his development. Speaking on behalf of Brian's character would make for a great theme and thesis for your literary analysis.