It is bitterly ironic that in this story, after Phoenix Jackson has overcome so many barriers and events that threaten to prevent her from reaching the surgery, the most significant barrier she faces is actually in the surgery itself, coming from the prejudice that she has to confront. If we examine when Phoenix finally enters the surgery, note how she is patronised and insulted by the attendant who speaks to her. The first thing the attendant says is "A charity case, I suppose," clearly indicating the prejudice against poor blacks. Then note how Phoenix Jackson is addressed:
"Speak up, Grandma," the woman said. "What's your name? We must have your history, you know. Have you been here before? What seems to be the trouble with you?"
When Phoenix does not respond to such patronising words, the attendant assumes that she is deaf, shouting at her. Thus one important example of irony in this excellent tale is the way in which the biggest challenge that Phoenix Jackson faces is not the hunter, the animals, or nature itself, but actually the challenge of racism and prejudice, as she is patronised and mistreated most when it appears that she has been successful in her quest and faces no more barriers.
This question has already been asked and answered here on eNotes. Here is a link for you: http://www.enotes.com/worn-path/q-and-a/what-irony-worn-path-103739