This quest is very possible to solo but should challenge most. If you take a group with you the ending becomes harder to balance with the group size.
Go to the Tartarus island city of Drakur and talk to Earl Godwin on the dock. He is looking for help hunting down and slaying Vikings.
Earl Godwin and his followers watch the movement of Viking ships in case of invasion. Many of those ships flounder at sea and he can give you a Salvage contract for them [No Fishing skill required].
If you get to the location of a sunken Viking ship you may be able to salvage Viking items and the Captain's Booty Box.
The Booty Box will of course have booty but will also contain the Captain's Log book. That book will indicate the location of the Viking outpost from which it sailed.
If you get to the Viking outpost you should clear it of any Vikings you find there. In doing so you can get the location and an entry pass into Avaldsnes [the Viking main settlement].
When you arrive at the entrance to Avaldsnes talk to Torstein the guard on the dock. If he is satisfied he will let you pass through. Avaldsnes is a larger encampment which is fortified and protects the King. Slaying the outpost bosses and the king can get you some interesting things.
This quest has a 5 hour cool down period and must be completed within 10 hours once you accept it.