Dark, ghost and bug. But be careful, as Phycic Pokemon can hit ghost Pokemon hard as well. Dark types don't get affected by phycic attacks, but, although there are no dark-types around, use dark type moves like bite and crunch.
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Dark type are very strong to physic pokemon. Grass,fire and water are weak(not very strong).
Koga, the Fuchsia City gym leader, is a Poison Type Pokemon trainer. Go into battle with ground and psychic type Pokemon. The Pokemon he uses are 2 Koffing, one Muk and one Weezing. Bring a Diglet/Dugtrio, an Abra (Kadabra/Alakazam), Drowzee and a Chansey if you can get one (Chansey is a super strong Pokemon that can learn TM Physic).
Grass type Pokemon are strong against Water, Ground and Rock.
Bug-type Pokemon are strong against Grass, Fighting, and Ground-type moves.
If you have any friends with ruby, sapphire or emerald or firered or leafgreen have them trade you really strong Pokemon then beat the elite four like that.