You are clearly not an idiot. However, exactly what is going on matters a lot. She sounds confrontational, nasty and pretty $(%*ing toxic. I have no idea, you left out lots of details. But it sounds like insecurity and jealousy. Jealousy can be based on perception too. If she thinks you are more confident, have a better man (BF), better in school, sports, dress better or even look better. If she is dumb enough to make it up she can convince herself it is real.
Like I said, while more information could have been provided: How is she aggressive, what started it, when, did you notice problems at the start (what), does she need to be center of attention - what did the 3 page letter say that sounds psychotic (lol). You seem pretty mature and intelligent - you might not be and you could be a troll. I will assume that is untrue though (troll).. Unlike most people are or will tell you ignoring her won't make it go away. You have been doing this, trying to ignore her and make effort to do the right thing to calm her down. Is it working?
Typically it makes it worse. You said a few interesting "text book" (typical) things. Why ignoring her won't work is pretty simple. She is trying to hurt, isolate, humiliate you (possibly a few other things). She is enjoying your reaction (passive, no action, apologizing; accepting blame). I'd assume she was never really a friend could that be true? I am sure she is not very smart but she might have saw you were someone she could use. The worst thing you can do is ignore/avoid her.
The more she pushes you or tries to hurt you the bigger and stronger she feels. When you do not do anything she uses this to justify her action (look she is letting me) and makes her feel stronger / more in control. I do not know if you could kick her $#% if you really needed. But it is pretty clear despite a big mouth, tears, lies and drama she probably won't show up at your house with a bat. She is enjoying the verbal stuff. The longer and harder she pushes you down the more it validates her. Like you noticed she wants to do it in front of groups (public). She wants to impress people, project power or just get their attention. Everything she says is probably a lie. She does it publicly because others see (or hear it). When they see you doing nothing they assume she is right about what she says and she is better and you were weaker. Even if they know it is not true your boyfriend, friends and her friends hear her starting this drama and know you are not directly trying to stop it - This is great for her and 100% what she wants / needs. Its like a high/hit off a joint. The longer you do nothing the more she feels she is winning. People will begin to take her side and that is the plan.
Does that make sense? She is getting off on and enjoying her perception she is in control and you are scared/won't do anything. She needs people to see this (so she engages others). You see and feel this right? Even if she is not getting it, eventually she probably does. She is doing it to be accepted by the group and isolate you. You need to take that 'control' away. There are 100 things you might do depending on her.
You don't allow some nasty wh*re or ignorant b*tch do this. The longer it goes on the more they see/think its working and it does get much worse. You stand up a bit. It is technically "stooping" to her level. Really though it is pushing back on drama and garbage.
Dress better and look better than she does. If there is anything you do better throw it at her publicly when you can. Better at sports, have nicer clothes, more confident or better grades who knows. Mention these things when you are near her - Especially when other people are near. You are not being rude or mean. You are reminding and showing her you are just as good (actually you are better). With your male & female friends you want to be more memorable. Think about TV shows we love the "mean girl" type shows with drama and jealousy. People naturally remember those type of people. You want to be a bit more memorable. Anything to make yourself stand out, be over the top helpful, be around them more often, ask for their opinion on things (clothes, projects, music or book you want to read). It is not needed but flirting or being more playful is great.
You are not remotely being aggressive. Just slowly taking her spotlight over 3-4 weeks. You are stepping in showing people you are great, making yourself more positive & memorable. You are pushing back at her with jealousy which also sends a great signal to others (you are as good or better). Your BF sees this too. Its good to see your girl stand up.
You do not trash talk her. But every time she says something negative or you hear about it. You must reply. Replying when she is there infront of a group is best (almost necessary). "I heard X" - "You know that is not true". You are shutting her down. Even if fake you want to appear more confident and secure. Notch up the jealousy where you can looking/feeling/doing better than her. Ask your man if he prefers a GF who stands up for him and herself or one who does not. People respect this, a leader does that. With your BF (man there, if he is jealous type) talk to her BF. Don't flirt but be overly polite, listen, smile - he is a part of her. You can't avoid him either. Guys talk, he might on occasion say good things to your BF. He will realize all the BS she has been saying is garbage.
There is a lot you do, just depends whats going on. That is my general thoughts when I've helped others before. While it is stooping to her level she clearly cares about her social image. Anything you can do to embarrass her really shuts her down and picks you up. None of this is violent. It is aggressive but not in your face. It is playful, fearless and "passive aggressive". You are not looking to fight. Wish you told us more. It is really tough might really take 3-4 weeks of escalating things like this. Eventually your friends naturally look to you and ignore her (which she will hate). You could hurt her at that point (revenge). but that really is not needed.