Evil Gods

Evil Gods are high-level monsters that inhabit the barren frostland of Jotunheim. 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 that's then only way to get the amount of money Kirito had. After Leafa and Kirito are caught by a trap do both types 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 Jotunheim by a trap, and Kirito and Leafa encounter a fight between a two-headed giant evil god and beast evil god. Upon Leafa's request Kirito aids the beast evil god by cracking the ice and causing both evil gods to fall into the water where the beast 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.