The Duel in Antarctica was a training activity that occurred between Gilgamesh and Thena while they were living in Antarctica.
Background[]

Ten Eternals were sent to Earth to protect the human population from Deviants. They moved around the planet, working to protect people and killing the Deviants they could find. Their search culminated in a large battle in Tenochtitlan, where they defeated what they believed to be the last of the Deviants. However, that night, the Eternal Thena developed Mahd Wy'ry as something went wrong with the erasure of her memory of her time on Centuri-Six. Thena attacked the other Deviants, but was taken out by Gilgamesh.

Thena was taken to the city, where Ajak determined that the only way to treat Mahd Wy'ry was to completely reset Thena's memory. The rest of the group was upset by this, but Ajak remained firm that it was dangerous to let her keep her memories. However, Gilgamesh refused to accept this and insisted that he would take care of Thena. Ajak agreed to this and,[1] following instructions from the Celestials,[2] told the Eternals to remain on Earth.[1] Gilgamesh and Thena moved to Antarctica together, finding it to be cold but enjoying their hot meals. They decided to continue training in case the Deviants returned.[3]
Duel[]

Thena avoids the cracking ice
Standing outside, Gilgamesh and Thena taunted each other. They powered up their weapons, and Gilgamesh punched the ground, causing a large crack to form in the ice. Thena jumped out of the way before the cracking could reach her and flew over Gilgamesh, attempting to hit him with her weapon. However, the weapon had no effect on Gilgamesh's exoskeleton, and Gilgamesh punched Thena, sending her flying backward. The two then charged each other, but briefly stopped to let a pair of penguins get out of the way.

Gilgamesh lays in defeat
They resumed fighting and faced each other again, but Thena claimed to see a Deviant behind Gilgamesh. This got Gilgamesh to turn around, allowing Thena to knock Gilgamesh off his feet. Gilgamesh groaned as he was defeated.[3]
Aftermath[]

Thena and Gilgamesh leave Antarctica
Thena stood over Gilgamesh and helped him to his feet as the pair agreed to leave Antarctica and move somewhere warmer.[3] They moved to Australia, where they lived an isolated life in the desert for years. However, Gilgamesh occasionally needed a break, so he once asked Druig to put her to sleep so that he could go on vacation to Fiji. They continued to live together as Thena's Mahd Wy'ry worsened.[1]