A Sigil Hall is a challenge similar to a gym, except run by Elite Four members and unique to the Vesryn Region. Only trainers who have defeated the Quasar League can challenge the five Sigil Halls of the Vesryn Region. The first four Sigil Halls can be battled an infinite amount of times, but Red's Hall of Legends can only be beaten once. (However Red can be rematched when using Tesseract at where he used to be). Sigil Halls are very difficult challenges that require incredibly strong Pokémon.
The Hall of Victors is located in Dojran City, at the base of the Vesryn Spear. It is accessed by speaking to the sign located in the middle of the town and is run by Tobias, a Dark type trainer. The Hall of Victors is the first Sigil Hall accessible in the Vesryn Region storyline.
The Hall of Heroes is located in Maggiore City and is run by Corlett, who trains Electric type Pokémon. Some of his Pokémon have modified movesets in order to make the Sigil Hall more difficult, such as his Eelektross, which knows Ice Beam.
The Hall of Champions is located in Skadar City and is the third Sigil Hall in the Vesryn Region. It is run by Water type trainer Morgan, the third member of the Elite Four. The HM Dive is required to access this Sigil Hall until the Scuba Gear is found.