What material are the shingles made out of?
Safe Restore or Lime Away
Here is a video to help you out. Best of luck!
Hi William: A good cleaner for calcium is vinegar. It works great for getting the calcium out of humidifiers, and buildup on shower heads, so it should work on your shingles. Spray the area and use a stiff brush to scrub, starting from the bottom and working your way up. This way you will eliminate the vinegar running down and leaving clean rivulets on the lower area, which are hard to get rid of. If it's clean vinegar running down, no problem :)
Here's a site that may help:
I assume you tried power washing it
Power washer vinger baking soda or borox