As a teenager, she would tend to be egocentric (think that others- adults do not understand her or what she's going through) When you speak with her, it may be helpful to focus on what she's experiencing (what she tells herself and what she believes) You can talk to her in a way where you let her know that you may not know completely what she's dealing with because each person has unique experiences. Yet, you've once been a teen and you're reminding her that as her mother, you're trying to have an open and honest relationship with her, and that you'd be there for her no matter what. Explain to her that you're not seeking disclosure that would make her feel uncomfortable or intrude on her privacy but rather wanting her to shed some light onto what is motivating her (what is behind her behavior)
You can explain to her that sexual intimacy does not necessarily translate into love or respect (it can be opportunistic for people) and that self worth is something that is not derived from external things (relationships/sex) but something one possesses within. Even though she's told you that she does not care what others think of her, you realize that her attempt at independence does not necessarily lead to increase in self worth. What matters is how she feels about herself and her actions and that is what you're talking to her about. Relationships and other's opinions come and go and what she carries within herself is something that she alone is in charge of.
You're helping her learn as the adult and parent in her life. Try to find out how her mood is (if she's depressed and drinking as a result of it or if she's doing it because her peers are doing it) You're being supportive to her and educating her at the same time and she may realize that everyone makes mistakes and that you're able to separate the person from their behaviors.