After getting the bow from the quest "Touching the Sky" you will actually get 12 Sunhallowed Elven arrows and 12 normal elven arrows.
The trick is to equip the Sunhallowed arrows and your Auriel's bow and shoot at the sun. I myself left the caves and as soon as I got out I equipped them both and shot at the sun. You'll get an achievement and quite few fireworks after doing it, and it will take about 3 seconds for the special ability trigger, after which you'll almost instantly get your achievement.
The way KillerBEA described it works the same way, but I was too hasty to wait for tainted arrows.
It seems as if you won't be able to get tainted arrows unless you side with the vampires, but for more sunhallowed arrows you'll have to go back to the elf that's in the place where you killed the Arch-Curate. He'll craft them from your elven arrows for no cost.