With the first of the legendary birds caught, let's hunt down the second. Like with Articuno, it's best to bring a large supply of Ultra Balls. To reach the Power Plant, venture east from Cerulean towards Rock Tunnel, then surf south along the river. It's not far to the end, where a lone PokéManiac is hanging around outside the building.
This old abandoned building still has a few items lying around, but beware: some of the items are actually Voltorb and Electrode in disguise. Just past the entrance room is a Carbos, and further along is a second "item," a Voltorb. The room to the east is a dead-end with both a Voltorb and Electrode, just waiting to pounce on an unsuspecting Trainer. Continue south to the exterior wall, and pick up TM33 (Reflect). Head to the east, and grab TM25 (Thunder) in the southeast room. Follow the narrow hallway to the north and west to find both a Rare Candy and an HP Up in the northeast room. Continue west and zigzag a bit to reach the final room.
Zapdos, the legendary bird of lightning.
Zapdos makes its nest in the deepest room of the Power Plant. Like with Articuno, be sure to save your progress before battling it. It won't go down without a fight, so whittle its health down and try inflicting a status condition before attempting to capture it.
In the time it took to collect the seven other badges, the leader of Viridian Gym has finally returned. None of the locals seem to know the identity of this mysterious figure, but it's certainly a familiar face.
Giovanni returned to his Gym Leader position after his defeat in Saffron City. His Gym turns out to be a favorite training spot for those who favor Ground-type Pokémon, so Grass-, Water-, and Ice-type attacks will see the most effectiveness. Flying Pokémon will be immune to Ground-type attacks, as well. However, Water- and Flying-types should be careful around Nidoking and Nidoqueen, since they both know Thunder, which can be fatal for them if it hits. Flying-types like Charizard should also be careful with Rhydon, because its Rock Slide can be dangerous to them. Also beware of Dugtrio and Rhydon's Fissure and Horn Drill, because if one of them manages to hit your Pokémon, the result is an automatic knockout, no matter how strong they are!
Congratulations on defeating the eighth and final Gym! The Earth Badge commands attention of all Pokémon, regardless of level. Giovanni gives you TM27 (Fissure), a TM he claims to have made when he originally acted as Gym Leader. He seems remorseful of his actions with Team Rocket, and officially disbands the gang before disappearing.
With all eight Gym badges collected, the way to Indigo Plateau is finally open. Gather a team with access to Surf and Strength, and stop by a Poké Mart to replenish your supply of Potions and Ultra Balls. The elite Trainers at Indigo Plateau are tough enough, but you'll never defeat them if you can't first get through Victory Road, a grueling tunnel with the third legendary bird roosting deep inside.