This quest is a daedric quest which has the Masque of Calvicus Vile, which helps with speechcraft and magica regeneration, as a reward or the Rueful Ax that does stamina damage. I started it by traveling to Falkreath and a guard asked me whether I had seen a dog. However, you can also start it by going to the smith, who you can find straight down the road you load in on. Ask him about a lost dog and the quest will start.
Next you have to find a dog outside Falkreath. I did this quest twice and both times the dog was within 10 meters of the quest marked a little further down the road.
The Location Barbas Leads You To
He will ask you to follow him. I did this initially but eventually he bugged out and kept leading me forwards and backwards. He actually leads you to Haemer’s Shame, which is west of Riften and south-east of Whiterun:
Once you go inside the quest marker will change. You have to go through Haemar’s Shame and through Haemar’s Cavern. At the end you will find the Shrine of Clavivus Vile. On the way you have to kill some vampires. I don’t have any trouble with them as I usually killed them with one hit. You can also easily sneak past them because they are to the side of the main path.
I had a little trouble with the last fight because there were a number of enemies. I used my strategy of focusing down weaker opponents to reduce the incoming damage and then I went after the tougher targets.
Retrieving the Rueful Ax from Rimrock Burrow
Calvicus Vile will ask you to retrieve the Rueful Ax from Rimerock Burrow which is located west of Solitude:
The only problem I had here was killing Sebastian Lart. The first time I went in here he killed me instantly once he saw me with fireballs. The easiest way to kill him is to range attack him until Barbas runs forward to help kill Sebastian Lart. He will take all the damage but he can’t be killed. Then you can safely go near Sebastian Lart and kill him. Be sure to stay away from Barbas because the lightning and fire damage has a certain radius. The Rueful Ax is on the table on the upper part of the cave.
Choosing Your Quest Reward
You can have either the Rueful Ax or the Masque of Calvicus Vile. If you choose to kill Barbas you can keep the Rueful Ax. If you don’t you have to return the Rueful Ax but receive the Masque of Calvicus Vile which grants 20% better prices, +10 Speechcraft and +5% magica regeneration. It also has an armor rating of 84 compared to a deadric helmet of 119. This is different depending on your perks and armor skill level, but the Masque of Calvicus Vile is only slightly less powerful than a daedric helmet.