Most of these Pokémon can only be obtained once per game; however, some may also be obtained in other ways as well.
List of Pokémon
Hisui first partner Pokémon
One of these Pokémon is given to the player by Professor Laventon after they are recruited into the Galaxy Team's Survey Corps. They must pick one of the three to obtain; after completing the main story, they can talk to Laventon to obtain the two that they did not pick. They also become available in space-time distortions, where they are not Shiny or alpha locked, unlike the ones from Professor Laventon.
This Spiritomb appears in the Shrouded Ruins after Request 22: "Eerie Apparitions in the Night" has been completed. After the request has been completed, there is a small chance for additional Spiritomb to spawn in the same place as the first; unlike the first Spiritomb, these have a chance of being Shiny or alpha Pokémon.
There are 28 Unown (one of each form) that appear throughout the Hisuiregion after the player gains the ability to rideUrsaluna. Their locations are hinted in the Unown Research Notes. These each remain stationary in a particular location where they can be caught, though they cannot be battled. After all 28 of the Unown have been captured, Unown of all forms will spawn inside the Solaceon Ruins, where they have a chance to be alpha or Shiny.
These unique alpha Pokémon can only be found once during the storyline. With the exception of Vespiquen, they do not have the usual guarantee of any stats with individual values of 31 (starting effort levels of 3). The alpha Pokémon found in Acuity, Verity, and Valor Caverns are prevented from being Shiny, and have Scale values of 127 instead of 255. Hisuian Zoroark and Overqwil do not have other fixed alpha spawns on the map.
Kricketune
During Mission 5: "A Request from Mai", the player is tasked with either defeating or catching an alphaKricketune that has been causing trouble in the area.
Three Phione appear in the Seaside Hollow during Request 66: "The Sea's Legend". After the request has been completed, there is a small chance for additional Phione to spawn in the Seaside Hollow, though these, like the Phione in the request, cannot be Shiny or alpha. Due to an oversight, Phione's scalar values are not locked when spawned in-game.
Dialga and Palkia are both obtained towards the end of the main story. If the player chose to get help from the Diamond Clan, they will battle and catch Dialga normally during Mission 17: "Atop Mount Coronet" and later catch Palkia in the Origin Ball during Mission 18: "The Counterpart"; this order is reversed if they chose to get help from the Pearl Clan instead. In the latter case, Dialga is quelled in its Origin Forme, but it will not remain in this form when caught.
Palkia and Dialga are both obtained towards the end of the main story. If the player chose to get help from the Pearl Clan, they will battle and catch Palkia normally during Mission 17: "Atop Mount Coronet" and later catch Dialga in the Origin Ball during Mission 18: "The Counterpart"; this order is reversed if they chose to get help from the Diamond Clan instead. In the latter case, Palkia is quelled in its Origin Forme, but it will not remain in this form when caught.
Giratina appears in Turnback Cave in Request 91: "On the Trail of Giratina". Unlike Dialga and Palkia, Giratina will remain in its Origin Forme once caught, as the player will also obtain the Griseous Core it possessed.
Arceus is obtained at the end of Mission 27: "The Deified Pokémon" (the game's final mission). It can only be fought after the player has obtained every Pokémon in the Hisui Pokédex (besides Mythical Pokémon), and it is obtained following its defeat.