The fourth and final test is the first real puzzle. There is an odd column that is emitting four spirits onto several spirit anvils. This is really more of a puzzle than a battle, if you do it right. The spirits should only attack you if you attack them. So for now, you can just work your way around the circle killing the spirits. When you kill one, it will power up the spirit anvil. You might only be able to kill one in each turn of the column. It's not a big deal. Just keep going.

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The one important thing to note is that AI is a little odd here. The party seems to want to attack the column itself, but they can't. So they just stand at the center. You'll need to keep ordering them around throughout the fight. Once all four are lit up, we get to do something cool. Pause the game, and then order each of your party to touch one of the four anvils. This will simultaneously hit all four sides of the device. The benefit to do it this way is that we won't risk getting off beat. It's just simpler this way. Note that the forgotten spirits will probably attack all together. Stick together and wait a moment until they get sucked back into the device.
We now have to deal with enraged spirits. These guys are a little more dangerous and we're going to go ahead and mix up our style. Hitting it now will completely knock out the side, which means no more spraying attack. Just pick a side and gang up on the spirit to reactivate the anvil. Fire it quickly and just wait. Unless you killed this one quickly, you probably wouldn't be able to take the next out in time. Catch it on the next rotation. Keep this going until you hit the fourth side and shut it all down.
This should finish it up. The door on the other side of the cavern should open. Save and then head out. We get to make our really big decision.