Pokémon Scarlet Hardcore Nuzlocke - SHINY Pokémon Only! (No items, No overleveling)

Can I beat a Pokemon Hardcore Nuzlocke challenge in Scarlet and Violet using only Shiny Pokemon? 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 Custom Rules - No setup moves - No terastalizing #pokemon #nuzlocke #shinypokemon