Think of stepping the court only when you are dragged into it. Don't waste your time collecting evidence from the point of view of court. However genuine your evidences are, we can prove it false. Also, even if you don't have a single evidence, we can still get the truth out from her itself. So as mentioned earlier, don't waste your time collecting evidence. Having said that, if something comes and falls on your lap don't ignore it too.
For eg. Even if she went to a hotel with a guy, she can always say it was official meeting. WRT chats etc. you can't prove that the other side is some guy.
As of now I still see lot of options.
Always remember, "Barking Dog seldom bites". She is threatening you not to leave because she is insecure and scared that her parents or others will know about her.
If you are done living with her, pack your bags and vacate the place. If she threatens, tell her you will file a complaint on her with the Police for blackmail and threatening. Also tell her that the first thing you will do is call her parents and inform them about her sexual encounters and affairs.
If she is okay with these things, ask her to go and file any complaint she wants. Tell her you will go to media and tell everything about her affair. Also, if she goes to Police Station, make her realize that it's her dignity/modesty at stake.
Also, tell her that if she files a DV case, then you will make sure that she never gets married to anyone else.
"Attack is the best defense". You always have option. Only thing that is required is guts to choose it.
Make her realize that the only option left with her is to sort it amicably by departing ways. Tell her you will support her with any lies she intends to tell her parents as to why you both broke up.
Having said all these. Since you both have been living together, as a matured individual, talk to her and find out if the person she is involved with is black-mailing her or anything of that sort. You cannot assume these kind of things. Also, most the victims of blackmail don't reveal easily. So you got to be understanding and patient. Tell her you will forgive her as long as she doesnt't intend to continue. Give her couple of days to think and come out.
Before going the hard way, give the latter suggestion a try. Meanwhile you will get sometime to prepare yourself to come to some conclusion.
Do rate the answer as it will help us serve better.