Hester Prynne's character is dynamic, meaning, it changes throughout the course of the book. At the beginning, we see her as a proud, ostracized woman struggling with her lot in life. But as the book goes on, she gains strength, humility, confidence and peace. She learns to serve the community without bitterness, to make better her lot in life, and to provide a living for her and her child. Her changing character can also be seen in the changing attitudes of the townspeople towards her. At first they judged and mocked, reviled and rejected. But as time went on, they learned to love her and rely upon her services and kindness. Some even considered her an angel of goodness and light.
When considering her character, keep the changes that she goes through in mind. We can also infer that before the events of the novel even began that she was a beautiful woman with a strong mind, who followed the instincts of her heart, rather than society's dictations of behavior. Through her refusal to reveal the baby's father's name, we can infer that she is very loyal, true, patient and selfless, because she is willing to bear the suffering for her sin alone. She is not vindictive or bitter.
I hope that those thoughts help to get you started; good luck!