Right before Nancy goes after Senator Roark in Sin City: A Dame to Kill For, she injures her face with a piece of broken mirror.
Why does she cut her face like that?
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Nancy wanted to kill Roark, but knew she would need help. Marv was Nancy's 'unofficial' protector, he would do anything for her (evident from earlier in the film when he defends her honor).
Playing Marv, Nancy cuts her face and then blames Roark - which sends Marv into a rage thus giving her a perfect (if psychopathic) ally for the final attack on Roark's estate.
Also, if you want to dig a little deeper, perhaps Nancy has finally become her 'father', Hartigan, a relentless killer out for revenge, even down the scarred face.
Using a mirror is very symbolic, especially in films. The mirror (and other reflective surfaces) are usually used to convey a torn personality, to literally show two sides to a person's personality. Nancy makes her living from her looks, the mirror is very important before each show, but when she decides to make the choice to go after Roark, she has effectively abandoned her old life - she has no more need for the mirror.