For this you should use bow and arrows. Upon entering the arena through the fog gate, kill the non-hostile enemies on the ledge and progress to the edge of the right path. From up there you can aim at the defenseless boss down below at the far end of the area and kill her with arrows, avoiding having to get past Garl Vinland. Just be aware that the boss occasionally heals, so you should have a large amount of good arrows with you.