How would one write a critical analysis of Porphyria's Lover for a university level course?
To write about Porphyria's Lover for an advanced undergraduate or graduate course, first you need to choose some salient aspect of the poem, then decide on a critical approach, then do bibliographic research, and finally compose your essay.
The power relations between the narrator and Porphyria, and other themes concerning the situation of women and repression of their sexuality, are common themes in feminist and gender criticism. For a Lacanian or Freudian approach, you would focus on the narrator's madness. A theological approach, looking at the role of God in the poem would also be possible, as would a new historicist approach in which you researched news stories about men killing their female lovers in this period for background.
In writing papers at this level, you are expected to be familiar with the major secondary works on the poem (search the MLA bibliography) and find either a gap in the scholarship or an accepted position with which you disagree.