Should i tell me best friend that our mutual friend was talking bad about her behind her back?

Well first of all, you shouldn't be friends with someone you don't even like so much. Just because your other friends are friends with her, doesn't mean you have to be. Second of all, what were you saying to her when she was telling you this? You should have told her to quit being so judgemental about her because she's your best friend. Why would she think it was ok to talk about her to you like that knowing you guys are best friends? You should tell your best friend to watch her back and not put too much trust in that girl. She's a shady *********.