She doesn't want to cut off her tips? She can try doing a soap cap which is basically bleach/developer, diluted with soap, similar to a color stripper a little more invasive.. If she used black box dye to dye her hair, she may have to full on bleach it to strip the black. Or just find a color to match her tips and be done with it.
Honestly though, you should really have her go to a professional, even a school. Bleach is very tricky especially when you're trying to lighten from black.
I personally go to a Paul Mitchell school in San Diego and can say for the price PM Schools will provide the best options for her hair (without having to fry it off), and I highly suggest you have them fix the color and repair it with a conditioning treatment.