To be fair to her, her level of power is usually a lot more due to the nature of other people, than her own nature. This type will generally have an instinctive understanding of how to manipulate both the human need for belonging, and the equally strong need that most people (especially teenagers) have, to abdicate personal responsibility and the role of making decisions, to someone else.
A common Hidden Depth to the Alpha Bitch is that she is, deep down, actually quite insecure, tragic, sympathetic or even nice. Often, she'll have been spoiled rotten because she's the apple of Daddy's eye and his indulgence of her has gotten way out of hand to the point of inducing malignant narcissism - or, on the flip side, she'll be suffering from emotional starvation because her cold, selfish and distant parents have substituted material goods for actual affection. Often she'll be raised and bullied by a mother who is herself an ex-Alpha Bitch and who forces her daughter to follow the same path in order to compensate for her own failed and wasted life. Depending on whether Status Quo Is God, this revelation may lead to her becoming a Fallen Princess, or even to the Alpha Bitch and the heroine to bury the hatchet.
This type is often (although not quite always) a malignant narcissist, and Histrionic Personality Disorder is also common. If they weren't spoiled rotten by their parents, (or even if they actually were) their central problem is usually a case of emotional starvation. This isn't as ironic as it sounds, because they basically have a fandom, when what they've always really needed (but generally never received) is actual friendship or love.
Because this type generally operates almost exclusively via psychological and social intrigue of various kinds, as mentioned, less idealistic types claim that there is usually only one way to effectively deal with them. The reason why violence can work, is because usually issues of physical survival are way below the Alpha Bitch's level within Maslow's Hierarchy of Needs, and thus putting her in fear for her life typically is not something that she will have any concept of how to deal with. Whether or not violence is either practical (Is getting back at this girl worth getting expelled or suspended over?) or appropriate (Is what she doing worth reallypunching her lights out? Why not just give her a taste of her own medicine instead?) is a matter of perspective, especially since it could arguably make her counterattack much worse...unless you murder her that is. While this virtually never happens in fiction, there are occasional exceptions. Even on the rare occasion when this path is followed, the person doing so will never be male.