Can I beat Pokémon FireRed with only Bug Type Pokémon using Hardcore Nuzlocke Rules?

Normal Nuzlocke Ruleset:
1. Fainting = Death
2. Can only catch the first Bug Type Pokémon on each route.
3. Nickname Pokémon

Hardcore Nuzlocke Ruleset:
4. No items in battle (held items okay)
5. No leveling past the next gym leader/E4 (at the START of the battle)
6. Play on "Set" battle mode

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