While we are limited in space to discuss writing a character analysis essay in great detail, here are a few pointers to you get started. When writing a character analysis, what we are doing is examining how the author/screen writer/director characterizes the character, how the character is presented as a person. There is a long list of things we can think about and analyze to figure out what the character is like as a person. Here is a list of a few things to look for and think about as you are analyzing your character: What does the character do? Say? What are the character's motivations? How do other characters respond to that character? Do we think he/she makes good decisions or bad decisions? A fuller list of things to think about is provided in the link below.
One thing we can notice about the story in the animated film My Neighbor Totoro is that it is really a coming-of-age story. The older sister Satsuki experiences personal growth as well as spiritual awakening. Therefore, her characterization will, at least partially, be used to show her growth and awakening. For example, one thing we can notice is that it's not insignificant that the younger sister Mei is the first to see the soot spirit called Totoro. Therefore, what does that tell us about Satsuki's level of spirituality as opposed to her younger sister's? However, later Satsuki does see Totoro while she and her sister are waiting in the rain for their father's bus to arrive. What does that say about her spirituality now that she has seen him? Has she experienced a spiritual growth? What does it say about her that she gave Totoro her only umbrella?
Satsuki's reaction to the fact that the girls could not see their mother due to difficulties their mother ran into with her medical treatments while in the hospital can also show us things about Satsuki's characterization. For example, the news hit Satsuki much harder than it hit Mei as Satsuki is aware of what death is. What does Satsuki's awareness of death show us about the development of her character? Does it show that she's maturing into an adult, and that this is a coming-of-age story?
All of these things are examples of what you can think about to analyze your character. Once you've figured out your character's traits through your analysis, you'll then be able to write your essay. Depending on how long your essay needs to be, I would plan on writing about at least three different character traits that make up Satsuki's characterization.