Arguably, Hester Prynne's character shows many more instances of bravery than instances of shame. Her shame is merely implied to the reader as a consequence of her actions. The affair that she sustains with Reverend Dimmesdale results in a pregnancy and, as a result, she has to endure the judgements and prejudices of a backwards society that claims to be "holier than thou".
However, the fact that Hester refuses to disclose the name of the father of her child is the first sign that she is not a woman who can be manhandled easily. She has actually accepted her situation and she even defends her child. The only shame that could be directly applied to Hester is her fear of discovery- not for her, but for Dimmesdale's sake.
As early as Chapter II we get instances of this fact. If Hester were a woman who is very ashamed of herself, we would never see her behaving on her behalf the way that she does. For example, we see how Hester shows a lot of dignity as she leaves prison to go to the scaffold while a guard tries to manhandle her:
[...]she repelled him, by an action marked with dignity and force of character, and stepped into the open air, as if by her own free will.
We also learn that Hester is trying to hide te image of the child to hide any resemblance to her father, who is a Reverend in the settlement.
In a moment, however, wisely judging that one token of her shame would but poorly serve to hide another, she took the baby on her arm, and, with a burning blush, and yet a haughty smile, and a glance that would not be abashed, looked around at her townspeople and neighbours.
We can see here that Hester is quite a challenging woman. She is not made to be one of the typical "goodwives" that are described previously as women who depend entirely of social acceptance. Hester faces her enemies with a challenging glance, and with a courage that makes Dimmesdale-and even Chillingworth- look weak.
Moreover, as time passes, we notice that Hester makes the best out of her scarlet letter. Not only does she wear it consistently, but she also decorates it as much as she decorates her daughter's wardrobe, making Pearl stand out even more than she already does under the scope of the town.
This being said, it is a clear fact that Hawthorne, in creating Hester Prynne's character, wishes to emphasize the strengths of Hester in spite of the shame of her actions. She accepts her isolation, as well as the scorn of a hypocritical society. She accepts her punishment and makes the best of it. Moreover, she still sticks to her principle of not allowing anyone to know that Dimmesdale has committed any fault.
Therefore, Hester only changes from strong to stronger. We never witness a weak woman in her. If anything, it is the men of the story who show their true weaknesses and their incapability to accept them.