Is it just me or does everyone deal with this kind of thing? To get ahead at work, it feels like you have to kiss up to the department head. She doesn’t really like other women and on top of that, she...

Welcome to Life & human beings. It has always been as such. Also depends upon how long and which industry you are working... in?I.E.Medical/I.T./Engineering/Finance whatever... Doesn't seem fair but then again, what might not seem fair to you might be someone else's "That's fine as long as I get to.." whatever ladder you are trying to get to the top of. You are a Threat because you are working hard. Some people want to keep people down because of their selfish Egos,(it would hurt if you were to get past your supervisior in ranking at a job, right? Because, you are now the Boss, and she has to kiss up to you.) =)
Don't let her stop you, if you want to be Excellent at anything, you just keep working hard and you will find yourself on the path which will take you to the top, if that's what you want. This person is making you become more determined, whether you achieve what you want there or at another Job, she is making you resilient. You don't have to like her or her method. Stay focused  more