It's a phase.
I did the same thing. Anything to rebel but mostly...I hated water. I would even go as far as to turn on the water, wet my hair in the sink, fluff myself with powder and act as if I showered.
Hmmmm, what would have helped me? Stubborn, hormonal, rebellious teen????
She is still young enough to obey despite the fact that she puts up a good fight. Sit her down and tell her...We take showers in this family. We have good hygiene. No daughter of mine will be the stinky girl in class. Those are the rules. I won't nag you to shower daily. I won't even mention it to you if you be sure to do it on your own. You're old enough to (List things she can do...sleep overs, computer time, sports, etc) Along with being mature enough for certain things come responsibility. Taking a shower daily is not up for debate. If you refuse to shower, you are refusing other mature things like (re list things she is allowed to do) and you will be treated like a child. Then ask her if her getting to pick out her very own bath set is something she would like to do. Or maybe take her to the bath towel section of a store and have the talk there or if you know her taste, have a gift basket ready for her with the towel set in it.
Anyway, If my mom had taken time like that to lay down the rules and do something special for me, I may not have rebelled so much. She may still throw a fit but just keep putting the love out there. Some of it gets in.
It's worth a shot.