Instructions
Head into the Pokemon League headquarters on the Indigo Plateu and heal up your Pokemon at the Pokecenter. Save your progress.
Use a combination of Rock, Electric, Ghost and Bug types to defeat the next Elite, Will. He will start with a Level 40 Xatu -- this is a Psychic/Flying-type Pokemon, but it's very weak against Electric, Rock, Ghost and Ice types. Next up is a Level 44 Jynx, an Ice/Psychic-type which is weak to Rock, Bug, Ghost, Steel, Fire and Dark-types. Next is a Level 41 Exeggutor, a Grass/Psychic-type which is very weak to Bug types and also Fire, Dark and Poison. A Level 41 Slowbro is next, which is weak against Bug, Ghost, Grass, Electric and Dark-types. Will's last Pokemon is another Xatu, at Level 42.
Move on through to the next Elite, Koga. His first Pokemon is a Level 40 Ariados, a Bug/Poison-type which is weak to Flying, Rock, Fire and Psychic-types. Then he'll send out a Level 43 Forrettress, a Bug/Steel-type which is very weak against Fire-types. Next is a Level 42 Muk, a Poison-type which is weak to Ground and Psychic. This is followed by a Venomoth, a Level 41 Bug/Poison-type which is weak against Flying, Rock, Fire and Psychic-types, and then a Level 44 Crobat, a Poison/Flying-type which you can beat easily with a Rock, Electric, Psychic or Ice-type Pokemon.
Use Psychic, Flying and Water types to take care of the third Elite, Bruno, who specializes in Fighting-type Pokemon. His first three are a Hitmontop, a Hitmonchan and a Hitmonlee, all at Level 42, and all of which are weak against Flying and Psychic-types. His next Pokemon is actually a Rock/Ground-type, Onix, which is very weak against Water-types. Finally, he sends out a Level 46 Machamp, by far his most powerful Pokemon, a fighting-type which is weak to Flying and Psychic-types.
Head through to take on the final Elite 4 boss, Karen. She'll start with a Level 42 Umbreon, a dark-type Pokemon which is weak against Fighting and Bug-type attacks. Next is a Level 45 Gengar, a Ghost/Poison-type which you can beat using Psychic, Ghost or Dark-types. Karen then sends out a Level 42 Vileplume, a Grass/Poison-type which is weak to Ice, Flying and Psychic-types. Next is a Level 44 Murkrow, which is weak against Rock, Electric and Ice-types. Finally Karen uses a Level 47 Houndoom, a Dark/Fire type which you can beat with a Water, Fighting, Rock or Ground-type Pokemon.