Evil Gods

Evil Gods are high-level monsters that inhabit the barren frostland of Jötunheimr. There are two types of Evil Gods: beast-types and humanoid-types. The most prominent one being a beast-type, named Tonkii.

Background
They're first mentioned when Kirito hands over money to the Sylph and Cait Sith Lords since, at that point, it's only way to get the amount of money Kirito had. After Leafa and Kirito are caught by a trap, both types of Evil Gods make an actual appearance,

They are a key point in Caliber Side Story.

Fairy Dance Arc
First mentioned based on the sum of Yurudo that Kirito handed over to the Sylph and Cait Sith lords to fund their quest. First seen after Kirito and Leafa are transported to Jötunheim by a trap, and Kirito and Leafa encounter a fight between a two-headed giant-type evil god and beast-type evil god. Upon Leafa's request Kirito aids the beast-type evil god by cracking the ice and causing both evil gods to fall into the water, where the beast-type evil god has the advantage.

Caliber
During the Caliber events, the Evil Gods represent two different factions, the Humanoid type for Thrym and the Beast-type as the one protecting Alfheim.