More than anything, Isabelle just wants to be happy with herself. For more than half of her life, she had to deal with constantly being told that she was a disappointment and pretty much just a waste of space. While she has done her best to move on from that time, many of the things that she was told by her mother have had a lasting effect on her personality. She strives for excellence, spending most of her free time training, but she never feels content with the progress that she has made. She was chosen to be the leader of her own team, but despite having proven her skill in combat, she believes that ALIA would be better off with any of the other members being in charge instead of her. Even when she manages to accomplish impressive goals that the average person may not have been able to do, she can't help but feel that it could have been done better. She thinks that the only way to overcome these feelings is to try harder at everything, and that someday she might just reach a point where she can be satisfied. Her happiness will come when she stops constantly questioning herself and starts actually believing in herself.
Lyssa has aspirations that are similar to Isabelle's in that she wishes to improve herself as a person, but her reasoning is a bit more valid. If you're racist and bitchy all the time, you'll come to realize that nobody wants to talk to you. Lyssa has figured this out, and has been attempting to turn herself around. She has been declining on the bitch-scale as of lately and has actually attempted to become acquaintances with certain faunus without being an asshole. Of course, she is still overly confident in her combat abilities and will definitely get her ass kicked sometime soon because of it, so further change is on its way.
Vivian's mindset is a bit simpler than the others. She is an extremely social person and wants nothing more than to make new friends and enjoy life. Not many things really bother her, so she is constantly on a quest to have fun rather than try and better herself. Having to go to class is not fun, but if she becomes a Huntress, she'll get to go to all sorts of places and do lots of cool stuff. She is definitely looking forward to that.
Cassidy isn't really one to want many different things. He is content with what he has now, and how his life is going. Really, he just wants everyone else around him to be safe and happy. Seeing that makes him feel like everything is alright, and that's good enough for him. If anything, he desires to graduate so that he can provide such protection for all different kinds of people.