This is a great question, and I have just answered the same question for you based on "The Jilting of Granny Weatherall." You might like to compare and contrast the two strong protagonists in that story and in "A Worn Path." There are several similarities that are easily identifiable.
I think one of the characteristics that we associate with Phoenix Jackson is her complete stubborn resilience. She makes the walk "regular as clockwork" as the nurse says, in spite of personal danger and the long distance she needs to cover. She meets the obstacles that she faces in the story head on and these hindrances reveal that she is polite, imaginative, humorous, optimistic, courageous and sly. Consider how she responds to having a gun pointed at her:
She stood straight and faced him.
"Doesn't the gun scare you?" he said, still pointing it.
"No, sir, I seen plenty go off closer by, in my day, and for less than what I done," she said, holding utterly still.
Her central action, phoenix-like, in renewing her love for her grandson each time she makes her journey along the "worn path," indicates her outlook on life, which is characterised by impressive determination and stoicism.