The character Pearl of Nathaniel Hawthorne's The Scarlet Letter acts as a symbol and is not rendered human until the final chapter of the novel as she kisses the lips of her father and "a spell was broken." It is only then that Pearl attains the ability to "grow up amid human joy and sorrow" and not "forever do battle with the world."
Prior to the concluding chapter, Pearl is the incarnation of the sins of passion that Hester Prynne and Arthur Dimmesdale commit. As such, she is a baffling mixture of strong moods: imaginative, inquisitive, intuitive, and obstinate at times. She demonstrates a fiery nature that battles with the other children and at other times is given to uncontrollable laughter. Because of the capriciousness of her nature, Pearl is referred to as an "elf-child," and "imp," or an "airy sprite" while some of the Puritans contend that she is a "demon offspring" perhaps because Pearl in Chapter IV:
writhed in convulsions of pain, and was a forcible type in its little frame, of the moral agony which Hester Prynne had borne throughout the day.
As evinced in Chapter IV. Pearl's responses to conflicts reflect the responses of her mother rather than any strength or weakness in Pearl herself. Because Hester Prynne demonstrates much strength as a person, Pearl, then mirrors this strength. For instance, in Chapter XIX, Pearl will not recognize or come to her mother until she replaces the scarlet letter that she has cast off into the brook. This strength of recognition that Hester must continue to bear her sin mirrors the words of Hester to Roger Chillingworth when he suggests that she may be worthy of having her scarlet letter removed by the magistrates,
Were I not worthy to be quit of it, it would fall away of its own nature, or be transformed into something that should speak a different purport.
That Pearl is primarily a symbol of the kind of passion which accompanies Hester's sin is well developed in Chapter VI; therefore, any strength that Pearl demonstrates--or any other emotion, for that matter--is a reflection of the nature of her mother, Hester Pyrnne, of whose passionate soul she is symbolic:
Pearl's aspect was imbued with a spell of infinite variety; in this one child there were many children....
Hester could only account for the child's character—and even then most vaguely and imperfectly—by recalling what she herself had been, during that momentous period while Pearl was imbibing her soul from the spiritual world, and her bodily frame from its material of earth. The mother's impassioned state had been the medium through which were transmitted to the unborn infant the rays of its moral life; and, however white and clear originally, they had taken the deep stains of crimson and gold, the fiery lustre, the black shadow, and the untempered light, of the intervening substance. Above all, the warfare of Hester's spirit, at that epoch, was perpetuated in Pearl.
Throughout the text Pearl grows in her ability to respond to conflict. She embodies conflict in the fact that she is the certral representation of the sin of both Hester and Dimmsdale.
Strength can have both positive and negative connotations. Pearl reflects the unending and undying effort of Puritans to reach a state of perfection. But, this is unattainable because all people sin. Pearl repeatedly presents that sin to Hester and holds Hester hostage to the sin. This type of accountability is certainly strength, but there is also strength in forgiveness, something Pearl is not willing to adopt.
I would argue that she is indeed strong because she deals with the adversity of other children, and she chooses her behaviors much to the dislike oftentimes of her mother.
However, strength can often be a character moral or virtue. If that is the area in which you wish to analyze her character, then I would argue that she is weak. The embodiment she was of Puritan culture demonstrates the truth of Puritans, they did not last as they were. Certainly, shades of Puritan culture still exist here today, but that quest for perfection (for which she tried to hold Hester to by making sure the A remained), allowed no room for mistakes and growing from those mistakes.