I feel like I'm kind of in a bad situation with regard to LORs. I'm incredibly shy and haven't built up a great relationship with my teachers. There are four teachers who I've had for two years (and a bunch of others who I had for one and never really formed a relationship with).
Of those four, one of them viciously hates me (I'll sit there silently and emotionlessly in her class and she'll just suddenly tell me to leave the room because I'm being disruptive, she regularly grades my tests incorrectly and refuses to fix it, and she often yells at me in front of the whole class for making minor mistakes on homework that's graded for completion even though she doesn't even pay attention to anyone else's work). One of them sponsors robotics (which I dedicate upwards of 40 hours per week to), but we have outside mentors who come in and supervise us and she doesn't supervise the club or have any clue at all that I'm even in it. The other two definitely value my work ethic and such, but I really don't have any relationship with them. I used to come to one of their rooms during lunch to do math problems, but now he sponsors a club during that time (I am in that club, but he pretty much just supervises while another students teaches about stocks, so it's not like anything there will reflect well in my letter). I've also been warned by some seniors not to ask him for an LOR because he doesn't know what he's doing with writing them. The other is an English teacher who has a reputation for writing pretty good LORs, but I'm not sure what he thinks of me. He definitely seems to admire me as a student, but he's told other people in my class that he thinks I'm too quiet. He's obviously right, but I don't know if that would become clear through an LOR (if it did, I'm assuming that would hurt my resume). I've also never been in any club with him or really engaged with him outside of class.

As for the clubs I am in, there are really only two of them that I'm particularly dedicated to. One of them is supervised by a teacher I've never had, and she just tutors students and we get the other half of the room, so obviously she's not paying attention to me. The other is, as I said, robotics, but that's supervised by outside mentors who are not teachers.

I'm a rising senior, so it's not like I have very long to change my reputation, and nor is "not being shy anymore" a reasonable goal to achieve within a couple of months. But is there anything I can do to improve the situation at all?