The suggested phrase is a little awkward, but I don't think that it is worth trying to figure out how to make it less so (and others have done this already, anyway), as the phrase just isn't idiomatic English.
I think that the idea is that the friend is a talented musician who can play many instruments, but getting that meaning from the proposed phrase requires one to know that the speaker earned a large number of As in high school. If that is the case, this comes across like a bit of a brag: "I earned so many As in high school, hence I can use this as a comparison for large numbers!"
Alternatively, it could be damning with faint praise—if the speaker were a poor student in high school, earning nothing but Bs and Cs (and maybe the occasional D or F), then the implied meaning is more like "Sure, he plays more instruments than I earned As in high school. Of course, I never earned a single A."
In either case, the focus of the comparison is unclear. Is it supposed to be about how many As the speaker earned, or how many instruments the friend plays? It is just a weird comparison (if you ask me). I would suggest trying to find a more idiomatic point of comparison. For example:
He plays more instruments than...
- ...a dog has fleas!
- ...there are stars in the sky!
- ...a beach has grains of sand!
- ...a forest has trees!
The first two are phrases which I have definitely heard in the past, while the latter two are (so far as I know) my own invention, but which are (I think) very likely to be easily understood by native speakers—the idea is to compare the number of instruments to some discrete quantity which is so large as to be practically uncountable.
Or one could ditch the entire structure of comparison (as suggested in the comments by TimR), and say something like
My friend plays so many instruments that...
- ...I need my fingers and toes to count them!
- ...I need a calculator to count them!