Right or left handed? There are a few extra steps for lefties as they have the added challenge of smudging.
Either way, getting a bunch of different pens is always worthwhile, along with a good paper. (You don’t get to choose the paper quality in exams but it helps for practice, and basically anything that helps the sensory experience will remove a barrier to practice.) The more a pen feels like an extension of your arm, the better. That won’t be instant, but some will feel better than others. Don’t waste any time with the ones that feel rubbish.
The most successful way to improve is one letter at a time. Doesn’t matter if you go in order or mix it up, but basically the first step is find the letter shape for each letter and repeat it hundreds of times. One letter a day is great for muscle memory, with a little review at the end of each session where you write all the letters you’ve done before, joining them together, just a few times. If there’s no visual cue there for what the letter shape should be, there are a few strategies. You can use a handwriting book, a font sampler, or look for examples from handwriting out in the world to just see what you like and then trace or mimic. (There’s a lot more freedom today in what is ‘good’ handwriting and essentially if it’s legible, it’s fine, so might as well model an example you like. Again removing a barrier really.)
Once you’ve been through the whole alphabet, then you start putting it into words. Doesn’t matter what words you’re using, so might as well double up the usefulness and do handwritten revision notes, make your own flashcards, etc. Part of the success path will be looking back at the handwritten notes and spotting what is looking good and what isn’t, then taking those letters back to the one letter a day step.
It’s old fashioned but it works, and I’ve used this pattern with all ages, from kids to pensioners, and the only times it hasn’t worked dramatically have been if someone gave up quickly or there was a secondary thing that we needed to go fix first - usually weak grip which at her age would be no problem to improve with a resistance ball/block to squeeze and release a lot, or shoulder pain that I would refer to physio or similar, and then come back to the steps when there’s no pain.
Good luck!