First of all, any good essay should open with a good introduction. In your introduction, you could give some examples of personal responsibility, in order to make it clear what exactly your essay will be about. One such example could be the responsibility a student has for the grades he or she achieves at school. Another might be the responsibility one has to treat other people kindly and respectfully. A third example might be the responsibility one has for one's own impact upon the environment.
In the main body of the essay, I would suggest that you deal separately with each of the examples given in your introduction. And for each example, you could consider how far one's personal responsibility might extend and what other factors or circumstances might increase or decrease one's personal responsibility. For example, when considering the student's personal responsibility for his or her grades, should we take into consideration the school that he or she attends? Does one student who attends a very good school have the same responsibility for his or her grades as a student who attends a very bad school? Also, to what extent should the teacher take responsibility for the grades achieved by his or her students? Is a good student with a good teacher in a good school as responsible for his or her own grades as a good student with a bad teacher in a bad school?
As regards to one's personal responsibility to act kindly and respectfully to others, is this responsibility decreased if the other person is deemed undeserving of kindness and respect? Also, is one's responsibility to be kind and respectful a responsibility mostly to ourselves or to society? Does our responsibility to be kind and respectful outweigh our responsibility to be honest, and, if not, which responsibility takes precedence when the two clash?
The third type of personal responsibility suggested above was one's responsibility for one's own impact upon the environment. Given that the vast majority of scientists tell us that human activity contributes to global warming, do we each have a personal responsibility to recycle, use public transport, and eat less meat? If we do, then why do so many people not accept or act on that responsibility? Is this responsibility actually a collective rather than a personal responsibility, and can collective responsibility be possible at all if people don't first take personal responsibility?
Finally, in the conclusion of your essay, I would suggest that you summarize the importance of personal responsibility, in part by addressing the following questions in relation to the examples you have discussed in the main body of the essay. Is personal responsibility a moral obligation? Are there circumstances or situations in which one can legitimately renounce personal responsibility, or, alternatively, in which personal responsibility is not possible? Where does one's personal responsibility end and a broader social responsibility begin?
Personal responsibility is an interesting focus for an essay. I wish you luck, and hope that you find helpful some of the above suggestions and questions.