Hello, I have medium auburn hair naturally. I dyed my hair a dark auburn but there is a section of my hair where the tips (two inches from root to tip) is almost black. I want to lighten these tips. Would using Peroxide Volume 20 mixed with shampoo do this?

No. You need to realize that peroxide (developer) reacted with the dyes to deposit the color in the hair. There's no way that using peroxide will get it out. You need to use color remover (ColorFix, Color Oops, Color Zap) to remove the color before you can lighten it. You may need to bleach it afterwards. Don't expect color remover to restore your natural color.