Once you've completed the main storyline, as well as the first post game dungeon and the boss there (three times), you will be able to access the second post game dungeon, The Ultima Thule, by heading back to the end of the Provenience Cavern in Paladurnia. Make your way through its levels to the top where you will encounter the boss of the zone and, much like the last post game dungeon boss, you will need to defeat them three times; unlike the previous dungeon, however, you will need to climb The Ultima Thule from level one each time.
Once you've defeated them thrice, they will be able to be spoken to as an NPC and challenged to a game of Esowa. They have many high level Berserker, Hero, and Assassin cards, so I recommend a strong offensive strategy. Open with berserkers and heroes of your own, being mindful of positioning to block off and destroy their pawns. Hold on to your Assassins for when you need advantageous positioning opened up or you need to remove a powerhouse. Gunners can also sit in reserve until they are approaching enough MP to use their special move. As for your own special move, pick whatever you have enjoyed up to this point; I found Reinforce to be the most useful throughout.
I'll include the deck I used to beat them first try, categorized by pawn type.
Berserker 4/5
- Lucifer x2
- Albel
- Asmodeus
Elite 3/5
- Ridley
- Laevonia x2
Hero 1/5
- Edge
Gunner 3/5
- Verda x2
- Reimi
Commander 4/5
- Lenneth
- Maria
- Evelysse
- Tika
Assassin 5/5
- Caleen
- Meracle
- Chisato
- Peppita
- Ernest