There are several types of critism that you could apply to this chapter. You might want to use the psychological approach to evaluate Chillingworth as portrayed through physical description/image. While you are doing this, you could do a textual criticism to show how the images that appear in this chapter reappear throughout the novel, and how/if they change as time passes. (Word processing software makes this a lot easier than it used to be.) This is sometimes called Formal criticism. You could also take the historical approach, exploring how the facts of the time are reflected in the novel (eg. why is there such a difference between the sentence Hester received and the one that she might have received if the rules of their society/religion were followed strickly). And, of course, you could study the use of irony in this chapter, clearly present in Dimmesdale's "oration" to Hester, but also present in the story of Chillingworth and Hester suggested in this chapter and developed later.
The one you select depends on your instructor. I think I would do the study of the initial images associated with Dimmesdale and then follow them through the book. Have fun!
I think it would be a good idea for you to take a feminist approach to the literary criticism you have to write. Considering Hester Prynne's experiences and the consequential treatment she receives from her society for her adultery, plus the incredible distinction between her actions and those of the man with whom she had the affair in terms of each one's accountability and courage to take society's punishment, a feminist critique would prove to have much depth as it could probably focus on the double standard and the castigation/ostracization of the female with little attention to the male's actions.