You will have to fight some, but you can avoid most of the fights in that dungeon and get the other half.
You have to fight a couple right away. After you kill them go clockwise around the big circle that makes up the dungeon. Don't deviate from the path. In the SE corner they is an inlet that you go in. Might be a gauth in there or on the way over. If you can go invisible or HiS, you can avoid some battles.
In the pond or pore or whatever is in the middle of that inlet is the other half. It becomes the rod, immediately equip it in your quick slot. Click on it cause as you leave the Uber Eye appears. Click it on him and it should take him down to near death(it did for me). Go poke him in the eye to finish him.
Go left and there are some stairs to take you out if you don't want to fight the big bad floating eyes anymore.
