'Asleifr has challenged you to a duel for the position of thegn of your clan.'
Something To Prove is a storyline quest which is started after defeating the Erlingsson in the previous quest, The Feast. Asleifr challenges the player character to a duel for the position of thegn which can't be refused.
Although all preparations steps can be skipped, it is advised to at least get the armour from Kveldulfr. However, a few points in the sense ability, or one rank in leadership, will be required to receive the armour.
You can also request the village hunter, Sigridr Manadottir, to lay a net trap in the upcoming duel, which will cause Asleifr to have his turn ended prematurely if caught in it.
Requesting the debuff potion from the witch, Hulda Crowtalker, is also an optional task, but she won't make much sense so it'll be up to her apprentice, Roskva, to make the poison. However, doing this will cause you to lose morale with Asleifr later if you choose to recruit him, and then recruit the Roskva.
You will arrive on the island with Nefja and Ketill, waiting for Asleifr to show up. This island is a rather small area, but contains two lootable items in the vicinity which you can search before or after the duel. The duel itself has three rounds; seemingly in advancing difficulty, but on lower difficulty settings the change is barely noticeable. You are able to fight the duel yourself or let Nefja fight as your champion, both lead to the same conclusion, with dialogue changing varying on your choices.
When you or Nefja has beaten Asleifr in three battles, you decide what to do with Asleifr. You can let him join your hird as hirdman, spare him, or exile.
You are awarded 10 power and prosperity when you finish the quest.
In case that you or Nefja are beaten three times, Asleifr wins the duel and the right to be thegn. The game does not end here, however, because Ketill intervenes and kills Asleifr by stabbing a knife through his back. His hirdman will try to avenge their leader, but their attempt is foiled by Sigridr and Lotjr, who kill them before they are successful. You can demands Ketills death for this unhonourable act or simply sweep this under the rug. Nefja will protest fiercily against your notion and convinces you to spare Ketill. In the end, you and the others decide not to inform anyone on what really happened on the island, except the lie that you won the duel in a honest way by killing Asleifr. This may have consequences later in the game, but they are not known so far.