I never heard that in any car with A/C, its like there's a coffee grinder in there.
Clutches might be an easier job but if its the compressor then it involves working on all the system, replacing fluids lost during the job, fiddling with vacuum pumps etc. Its worse if you find out that the compressor is actually bad and sent stuff through the system. That I know one of the first thing a shop would check is the charge and pressure, which noises also can sound similar to a grind.
A/C can be the kind of PITA job that is more convenient to let a shop do rather than yourself, even because of some particular tools needed. I'd bring it to the dealer if you have a decent one at hand.