Hyperspace Fury! Hoopa Transformation (Japanese: いじげんラッシュ！フーパ変幻) is the fourth set in the Pokémon Tretta Ultimate series, and the eighteenth overall. It features 48 Tretta.
Hoopa is once again featured as a prominent Pokémon in Hyperspace Fury! Hoopa Transformation, appearing as an Ultimate-class Tretta and in both of its forms. Hoopa begins Battle Mode in its Confined form and can use Hyperspace Hole, transforming into its Unbound form if still able to battle at the start of Round 3, with the ability to use Hyperspace Fury. This set also includes two Legend-class Tretta, which feature the New Species Pokémon Mew, its second time appearing as a Legend-class Tretta, and the Pokémon Tretta debut of the Time Travel Pokémon Celebi.
Locations included in Search Mode have an autumn theme, with Ruins and Park replacing Beach and Foot, absent for the first time since its introduction.
Hyperspace Fury! Hoopa Transformation also introduces a fundamental aspect of all core series Pokémon games to Pokémon Tretta: the ability to trade. Pokémon Exchange Time (Japanese: ポケモンこうかんタイム) may begin after successfully capturing at least one Pokémon in Catch Mode, during which a Tretta Leaguer may offer to trade for another Pokémon from the same set. The Pokémon available for trade are random and are not limited relative to the class of Pokémon caught. The player can choose to accept or decline the trade using the console buttons. The Pokémon ultimately selected will be dispensed and, if the player has a Tretta Report, will be added to the list of caught Pokémon. The score earned at the end of Catch Mode applies to the Pokémon caught originally, regardless of any trades.
Challenge Battle also includes five new line-ups for players to earn another five stamps on their Stamp Card, with returning faces including Tretta Idol Hitomi, Top Leaguer Tatsuya, and Legend Leaguer Goushou, albeit in a different cowl. Players with Tretta Reports could also add the Legendary Order Pokémon Zygarde to their Extra Attacker roster through repeated play.