I have been asked to do a literary criticism for "The Scarlett Letter," chapter 3. What type of criticism should I use?

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!