There is this women who is dating a friend of mine and I see her every now and then and she has figured out that I do PU. But she is always totally derisive towards me, she says things like

"You are not the kind of man that is attractive to women."

How do I deal with that considering she is dating a good friend of mine and I don't want to offend my friend?

She's just a hater. No big deal. Kill her with kindness. Don't make yourself look bad by getting nasty with her.

_________________
“Nothing is impossible, the word itself says 'I'm possible'!” ~Audrey Hepburn

You correctly pointed out that nastiness is not the answer, but I wonder if being kind is that much better. In other words:

1. Being just non reactive or kind makes me look like a tool.
2. Being nasty would be being reactive and risks jeopardizing my friend ship.
3. What is the 3rd missing alternative that avoids 1 and 2?

She's in territory where she doesn't belong, regardless.

If shit testing you, why?
If just being rude to one of her boyfriend's friends, why?

Did you in any way invite her to express her opinion or was she just rude on her own initiative?

I wouldn't advise kindness or nastyness, just polite non-engagement.

Be a gentleman about it..You don't have to discuss it.

_________________
In a funk? Read this

pua-lounge/the-importance-patience-this ... his%20game

Well it depends on the situation. Who else is around? What is the context of the conversation? Are you expected to respond to her derisive comments or can you just ignore it or change the subject?

I have kind of an aloof self-deprecating personality, so when people hate on me I'll just kind of go along with it, especially when I can tell there is mean-spiritedness behind it. Because they are obviously looking to start trouble or get a negative reaction out of you. When you laugh and are like "I know, right?!" then it makes it seem like they said something funny that amused you, and it totally steals their thunder. Deep down that pisses them off even more, but the beauty is they can't call attention to that fact because then they would REALLY make themselves look like hateful little mongers. That's the why they call it killing them with kindness.

_________________
“Nothing is impossible, the word itself says 'I'm possible'!” ~Audrey Hepburn