To get the boulder badge you must defeat Brock, the pewter city gym leader. If you picked Charmander i would suggest using metal claw or catching a Mankey and teaching it low kick.
the boulder badge from brock
fuschia.
Fuschia city.
In Vermilion city.
fap
you sneak into it and Get in there go get a rode and do it
vermillon city
Head to Cinnibar Island for your next badge.
Vermilion city.
The boulder badge, the cascade badge, the thunder badge, the rainbow badge, the soul badge, the marsh badge, the volcano badge and the earth badge.
The fifth Gym Leader in Pokemon LeafGreen is Koga, the leader of Fuschia City's Gym. He specializes in Poison-type Pokemon and hands out the Soul Badge.
You need the Cobble Badge.