I agree that it is very difficult to read, I only got about half of it and have always considered myself pretty good at making stuff out.
Does he manage better when writing on lined paper? How much can he improve if he slows down, and just how slow is it when he does?
If he's 13 then I'd want to be sure he is / gets good at touchtyping, and if his teachers are already not marking some of his work I would really hope that someone's started talking about having him do some of his classwork on a computer.
Having said that, as part of an assessment in ? year 6, the comment was made that my DS's handwriting was bad enough that he'd probably need to take exams later on a computer and to make sure he learnt to type. I didn't worry too much as he could type well already at that point. At some point the message that better writing was worth it finally sank in; and at age 16 it usually stays more or less on the line and can be read, he does a lot of work on his computer but can manage written exams fine. He can produce good stuff but finds it too slow to be worth doing.
I think the two things that make a difference to writing are, does it stay the same size, and does it stay on the line. You can get practice books with paired lines closer together - if you review which letters/parts of letters should fit within those lines and practice lining words up that way, it can really help.
Good luck to your son moving forward in the right (write?!) way for him.