I replaced mine a couple of years ago and remember it taking a lot of force to loosen the pulley. It was tricky holding the (relatively small) wrench in one direction while applying a lot of force with a larger breaker bar in the other direction. I was able to do it, so it is definitely possible.
Best of luck and let us know how it turns out.
ddb
Clicking Noise Solved (Alternator Pulley)