When the party reaches the entrance into Thyrmheim, Yui explains that the quest they started had been created by the Cardinal system's "Automatic Quest Generation System", which sought out mythological stories relevant to ALO and made quests based on them. According to the Norse mythology on which ALO is based, the events of the quest would lead to a destructive war: "Ragnarok", the Twilight of the Gods. If the party failed in their quest, the World Tree and Alfheim would be destroyed. No one seems willing to believe such a thing could happen, until Yui reminds them that the Cardinal system, upon which ALO runs on a near-exact copy, destroyed Aincrad in SAO in a similar manner when it was cleared.
With little time to waste, the party presses on.
On the second floor of Thymrheim, the party come across two powerful minotaur bosses, one resistant to physical attacks and the other, magical attacks, and both able to quickly heal from damage. Without a mage, the party relies on element-based Sword Skills to try and defeat the physically-resilient minotaur, but this leaves them wide open to attacks when they complete their skills. Kirito, however, has found a way to counteract his own post-skill cooldown: "Skill Connect". While ALO did not have a "Dual Wielding" skill like SAO did, he could equip a one-handed sword in each hand, then alternate between using Sword Skills in each hand. This allows Kirito to use Sword Skills in rapid succession before having to stop and cooldown. With this new technique, Kirito was able to lay the physically-resilient minotaur low. The magically-resilient minotaur fell easily afterwards.
On their way to the next floor, the party encounters an NPC trapped in an ice cage. The NPC has her own health bar, leading most of the party to believe it's a trap. Klein, however, becomes smitten with the NPC and, against the party's advice, frees her. Rather than run or fight them, the NPC, Freyja, thanks Klein for his aid and joins the party in order to reclaim a lost treasure, giving the party a massive buff in the process. With that, they proceed to fight the final boss of the quest, Thymr.