Practice.

Taking notes during lecture helped. Not only does it help cement the information in your mind, it is practice writing legibly enough it can be studied later. You could practice this now, before school starts, by watching something like Khan Academy.

If your major sends you to the whiteboard often, that will help a lot, too. You will naturally improve as you do it out of necessity. Practice on the board until you can write a straight line of consistent text that doesn’t droop or curve down as it goes along.

I second the suggestion for calligraphy in a script you like.

Perhaps practice by trying to quickly write down song lyrics as you listen? I think that’s when I first started to improve.

Pay attention to your classmates who can take good notes quickly. I made a friend who found my writing to be glacially slow, so I watched how they wrote to learn some tricks.

Sorry if some of these won’t help until you’re in, but don’t worry about it too much. I’m sure your handwriting will be markedly improved by the end of even the first year.