In fire red/leaf green it is in Cerulean City in sapphire/ruby/emrald it is in Mauville City
The second gym badge is obtained from the second gym you visit. However, each gym is different per game. For example, the second gym is located in Eterna City in Platinum but in Emerald, the second gym is located in Dewford Town. So which game are you referring to?
* Pewter Gym - Rock Badge * Cerulean Gym - Cascade Badge * Vermillion Gym - Thunder Badge * Celadon Gym - Rainbow Badge * Fuchsia Gym - Soul Badge * Saffron Gym - Marsh Badge * Cinnabar Gym - Volcano Badge * Viridian Gym - Earth Badge
Beat the gym leader.
You should get the second badge from Bugsy in Azalea's gym. If you can't get inside the gym, then you need to drive Team Rocket out of Slowpoke Well first.
The sixth gym badge is the Marsh Badge and is obtained when you defeat Sabrina at the Saffron City's Second gym. In order to gain access to this gym, you must first remove Team Rocket's presence in Saffron City by defeating Giovanni.
it is bugsy the bug type leader
its a normal type gym leader named lenora, gives out basic badge
8th gym badge the water badge
The second gym is located in Eterna City and uses Grass-type pokemon.
you can find it near the second gym badge and its in a cave.
the fourth gym is in celadon city at the bottom left of the city. the gym leader is erika. the badge is called the rainbow badge
volcano badge