I know that you can definitely take GCSEs outside of school. I took an Astronomy GCSE outside of school for example, but usually you do it through a college. There are adults doing GCSEs in their spare time, so maybe look around at local colleges/universities to see if there are any open courses and talk to them.
Also, how much background do you have with the German language? If you are a complete beginner then there is no way you will complete the GCSE course in 1 year to an A* ability. You probably studied it at KS2 if you are passionate about it. I would say if you have a background in a Germanic language e.g. Swedish, then that would help you pick it up faster, however I don't think it's possible to study a 2 year German course in 1 year, achieve an A* grade ON TOP of all of your other GCSEs. German is a demanding subject where the only way to learn is repetition and a lot of hard work. If you have a knack for languages it will still be a mean feat in just 12 months.
As I said before, check with colleges. However, I think you'll have to enrol in an evening course if possible, as well as or instead of your tutor. German GCSEs are graded on Listening, Reading, Writing AND Speaking exams. Whilst listening and reading are exams you can just turn up to, writing and speaking require supervised preparation sessions, and the speaking needs an assessor to sit down with you and have a conversation, record it, and mark it. This is far easier and smoother if done with your teacher, so I would recommend looking at proper courses instead of just trying to submit yourself into the tests and do all of the studying independently. So look at colleges, and definitely talk to your school's languages teachers - they may have some inside knowledge on it. Good luck, and you'll have fun with German! My favourite subject