Pokémon Violet Hardcore Nuzlocke - Fairy Types Only! (No items, No overleveling)

Can I beat a Pokemon Hardcore Nuzlocke challenge in Scarlet and Violet using only Fairy types? Nuzlocke Rules: -Fainted Pokemon must be permanently boxed -Only the first encounter on any given route may be caught (dupes clause) -All pokemon must be nicknamed Hardcore Rules: -Always Set mode -No items from the bag option in battle (held items are ok) -No overleveling the next gym leader Personal Rules: -No setup moves -No Terastalization #pokemon #nuzlocke #challenge