At the core of Nathaniel Hawthorne's novel of secret sins are passion and love. Certainly, there are incidences in which the love and passion that characters possess propel them into unselfish acts of love which serve to overcome certain spiritual obstacles.

1. At the end of Chapter VIII, Hester's love for her child, Pearl, overrides her deep depression and loss of faith.  For, when Mistress Hibbins invites her to enter with her the dark forest and join with the Black Man, Hester tells her,

"...I must tarry at home, and keep watch over my little Pearl.  Had they taken her from me, I would willingly have gone with thee into the forest, and signed my name in the Black Man's book, too...."

2. In Chapter XIII, Hawthorne writes that that "[T]he scarlet letter had not done its office." However, as Hester's despair continues and she wonders if she and Pearl were not better off dead as she "wanders without a clue in the dark labyrinth of mind," she is spurred by love once again. For, in Chapter IX she speaks with Roger Chillingworth, begging him to relinquish his formidable hold upon the minister's heart; she tells her husband that to do so would purge him, but he replies that the situation "is our fate."  Nevertheless, Hester resolves to warn the minister about Chillingworth and to reveal his identity. Then, with this new knowledge, the minister is incensed, telling Hester he cannot forgive her. In addition, he considers a new fear,

"Hester!...here is a new horror! Roger Chillingworth knows your purpose to reveal his true character.  Wilt he continue, then, to keep our secret?  What will now be the course of his revenge?"

Lovingly scolding him, Hester admonishes him, "Wilt thou die for very weakness?" Answering his request for advice, Hester tells him to leave the community and return to England, but he will not be alone:

"Thou art crushed under this seven years' weight of misery....But thou shalt leave it all behind thee! It shall not cumber thy steps....Thou shall not go alone!"

3. In Chapter XII, Pearl asks the minister standing in the dark on the scaffold if he will "stand here with mother and me, to-morrow noontide" and he denies that he will, "Not then, Pearl...but another time!"  But, Pearl does not wish to wait until Judgment Day; so, she toys with the minister, muttering gibberish in his ear, because he has acted falsely--"Thou wast not bold!"  However, when Dimmesdale does, indeed, stand on the scaffold on the New England Holiday and confesses his sin, having extended his hand to Hester and Pearl, Pearl rewards his confession with a kiss, transforming her from the "sprite" and "imp" that she is characterized as into a real person and "Pearl's errand as a messenger of anguish was fulfilled."

4. In a dying act of Christian love, the deformed physician Roger Chillingworth, whose heinous plan of revenge has been foiled by the minister's confession, returns to England. When he dies, it is learned that he has bequeathed 

a very considerable amount of property, both here and in England to little Pearl, the daughter of Hester Prynne.

His act of unselfish Christian love defeats his life of spite and revenge, thus saving Roger Chillingworth's eternal soul.

Critically examine The Scarlet Letter in terms of the theme love triumphs over various obstacles.

This sounds like a prompt for a critical essay. I encourage you to accomplish this assignment by spending the most time pre-writing, or gathering evidence, forming a thesis, and planning and organizing your essay. The theme of love triumphing over other various obstacles gives you two great subjects under which to gather evidence.

First, come up with a list of examples (use quotes where you can) of love triumphing. Certainly Dimmesdale's confession on the scaffold in the final scene of the story could be evidence of this. But there are several other examples as well. Hester's ability to remain a citizen of the town, raise her daughter alone, and eventually earn the respect of others (as the "A" comes to stand for "able") are all examples of love triumphing.

Then, think of examples of the obstacles that are overcome. Each character has his or her own set, so you can choose now or later to edit down your list by following only one or two characters. I always suggest gathering as much as possible so you know what you have to work with. To help you get started you might include that Hester must overcome shame and public shunning in order to move on with her life at all. Dimmesdale must overcome his own personal guilt, as well as live with the secret he holds.

Once you have two long lists, you can look at each and see if any patterns or categories begin to emerge. Circle ideas that are similar. Cross out ideas that seem to fit with nothing. Once you've edited down your list of examples into a few coordinating categories, use these categories to compose a thesis statement.

Now you are ready to outline your essay. Write a topic sentence for three body paragraphs (or more) that support your thesis statement. Include examples (from your original list) that support each topic sentence. Once you've accomplished these steps, the bulk of your work is done.

Feel free to post further questions here for help as you go, and good luck!