How to show people, that someone is not the person they think it is

Hi, I have this colleague at work, let's call her P, she always acts like she's very sweet, kind, good person, but she's actually very envious, hypocritical and fake. I know that because I'm the person who is working with her all the time (we're on the same position), while all other colleagues are not communicating with P that much about work. So I guess she's sharing her thoughts with me, because she knows me better, but she keeps the fake mask with everyone else.
Let me give you an example: another colleague of ours walks in the office and P is like "omg is that a new hair color? it looks amazing, it suits you, you look gorgeous and blah blah". That colleague goes away and 5 second later P turns to me and says "omg did you see her new color- it's awful.. she looks horrible".
And that's just one example, she's talking shit behind everyone's back and that makes me sick how fake she is.. I hate such people. And moreover I hear everyone saying about P that she's such a warm and good person, she's pure like a child, she's sweet and cute.. it makes me sick. I want to let them know she's nothing like that and she's talking behind their backs (which I'm sure she's talking behind mine too). But If I just tell them I think that won't make me any better person and I'm also scared they might not believe me, because she has everyone fooled. They probably think she's better person than me, because I don't fake compliment everyone all the time.. What should I do?