The Unfinished Business side quest is one of the many favors that you can complete in God of War. In this quest, your task is simply to help the spirits and: “Explore the islands of the Lake.”
Once you speak to the first spirit, you're warned that by lighting braziers enemies called Seior and Helwalkers “will swarm to the flames like moths.” You get awarded a Versatile Warrior's Handle, which increases your Strength, Defense and Luck.
Your map is updated and a new area is revealed. Light the first brazier and get ready to be attacked. Use your axe to kill the flying creatures first as they can be a real pain. Then defeat the ground enemies up close and personal. They only have swords, so they're easy to defeat.
Once they're all defeated, speak with the next spirit. You'll now be awarded a Corrupted Remnant, a legendary item which allows you to upgrade the Versatile Warrior's Handle. Light the next brazier, and fight the next wave of enemies.
Go back and speak to the spirit and you'll get another Corrupted Remnant. Light the next brazier and get ready for another fight. This time it's against yellow creatures with a tail that emerges from the ground. Use your axe to freeze them before they attack, and then move in close to batter them.
Now you've got to deal with the big dude with the club. Let him attack Atreus and when he has his back to you whack him. At one point, Atreus will jump on his back which is your cue to go in for the kill. Go back to the spirit, and pick up your final reward, another legendary Corrupted Remnant.
The Unfinished Business side quest is one of many optional missions in God of War. This one takes about 10 minutes to complete, and the rewards to completing them often allow you to upgrade Kratos further and make him stronger for future, much tougher battles.