After defeating the Elite Four and having become the newest Kanto Region Champion, you will be able to find a number of New trainers scattered across the region. These trainers are known as Master Trainers, and they specialize in battling with one specific species of Pokemon. Their Pokemon will be at a very high level, and some of them will even know moves that they can't usually know. Many of their Pokemon will even have had their Stats boosted with the use of Pokemon Candy, making them all the more stronger.
Because there are roughly a hundred and fifty Pokemon in the Kanto Region, that is the same amount of Master Trainers you will be able to find and battle apart of the Master Trainer Challenge. However, there is a catch to this: you can only battle these trainers with one Pokemon, and it has to be the Pokemon they specialize in using. After defeating any of the Master Trainers, you will earn the Master Trainer Title for that given species of Pokemon. The Master Trainers for all the Legendary and Mythical Pokemon (as well as Ditto) will only need to be found in order to earn the Master Title for those given Pokemon, but you will need to own said Pokemon at an extremely high Combat Power Level. After earning all the Master Trainer Titles, you can obtain the Grand Master Title from the woman inside the Game Freak Building within Celadon City.
Master Trainer Locations
Bulbasaur Master Trainer: Route 4 East
Ivysaur Master Trainer: Route 14
Venusaur Master Trainer: Route 23
Charmander Master Trainer: Celadon City
Charmeleon Master Trainer: Route 10
Charizard Master Trainer: Route 23
Squirtle Master Trainer: Route 12
Wartortle Master Trainer: Route 20
Blastoise Master Trainer: Route 20
Caterpie Master Trainer: Route 18
Metapod Master Trainer: Route 11
Butterfree Master Trainer: Route 2 North
Weedle Master Trainer: Viridian Forest
Kakuna Master Trainer: Route 13
Beedrill Master Trainer: Route 8
Pidgey Master Trainer: Route 2 South
Pidgeotto Master Trainer: Route 16
Pidgeot Master Trainer: Route 12
Rattata Master Trainer: Route 10
Raticate Master Trainer: Cerulean City
Spearow Master Trainer: Pewter City
Fearow Master Trainer: Route 18
Ekans Master Trainer: Route 4 East
Arbok Master Trainer: Rocket Hideout
Pikachu Master Trainer: Viridian Forest
Raichu Master Trainer: Pokemon Tower
Sandshrew Master Trainer: Route 11
Sandslash Master Trainer: Route 7
Nidoran(F) Master Trainer: Route 3
Nidorina Master Trainer: Underground Path 7-8
Nidoqueen Master Trainer: Route 23
Nidoran(M) Master Trainer: Route 4 West
Nidorino Master Trainer: Underground Path 7-8
Nidoking Master Trainer: Route 23
Clefairy Master Trainer: Saffron City
Clefable Master Trainer: Mt. Moon
Vulpix Master Trainer: Route 6
Ninetales Master Trainer: Route 9
Jigglypuff Master Trainer: Pewter City
Wigglytuff Master Trainer: Silph Co
Zubat Master Trainer: Rock Tunnel
Golbat Master Trainer: Victory Road
Oddish Master Trainer: Viridian City
Gloom Master Trainer: Pewter City
Vileplume Master Trainer: Route 14
Paras Master Trainer: Mt. Moon
Parasect Master Trainer: Route 2 North
Venonat Master Trainer: Route 24
Venomoth Master Trainer: Route 15
Diglett Master Trainer: Diglett Cave
Dugtrio Master Trainer: Diglett Cave
Meowth Master Trainer: Viridian City
Persian Master Trainer: Rocket Hideout
Psyduck Master Trainer: Route 21
Golduck Master Trainer: Route 4 East
Mankey Master Trainer: Route 5
Primeape Master Trainer: Route 11
Growlithe Master Trainer: Route 7
Arcanine Master Trainer: Celadon City
Poliwag Master Trainer: Route 12
Poliwhirl Master Trainer: Cerulean City
Poliwrath Master Trainer: Cerulean City
Abra Master Trainer: Viridian City
Kadabra Master Trainer: Saffron City
Alakazam Master Trainer: Route 10
Machop Master Trainer: Silph Co
Machoke Master Trainer: Fuchsia City
Machamp Master Trainer: Vermilion City
Bellsprout Master Trainer: Viridian City
Weepinbell Master Trainer: Pokemon Tower
Victreebel Master Trainer: Celadon City
Tentacool Master Trainer: Route 20
Tentacruel Master Trainer: Route 20
Geodude Master Trainer: Rock Tunnel
Graveler Master Trainer: Victory Road
Golem Master Trainer: Pewter City
Ponyta Master Trainer: Saffron City
Rapidash Master Trainer: Saffron City
Slowpoke Master Trainer: Route 21
Slowbro Master Trainer: Route 21
Magnemite Master Trainer: Underground Path 5-6
Magneton Master Trainer: Underground Path 5-6
Farfetch'd Master Trainer: Vermilion City
Doduo Master Trainer: Cerulean City
Dodrio Master Trainer: Route 15
Seel Master Trainer: Seafoam Islands
Dewgong Master Trainer: Seafoam Islands
Grimer Master Trainer: Celadon City
Muk Master Trainer: Pokemon Mansion
Shellder Master Trainer: Route 19
Cloyster Master Trainer: Route 20
Gastly Master Trainer: Lavender Town
Haunter Master Trainer: Lavender Town
Gengar Master Trainer: Lavender Town
Onix Master Trainer: Underground Path 7-8
Drowzee Master Trainer: Viridian City
Hypno Master Trainer: Pokemon Tower
Krabby Master Trainer: Vermilion City
Kingler Master Trainer: Silph Co
Voltorb Master Trainer: Power Plant
Electrode Master Trainer: Route 16
Exeggcute Master Trainer: Route 24
Exeggutor Master Trainer: Cinnabar Island
Cubone Master Trainer: Route 8
Marowak Master Trainer: Lavender Town
Hitmonlee Master Trainer: Saffron City
Hitmonchan Master Trainer: Saffron City
Lickitung Master Trainer: Route 16
Koffing Master Trainer: Route 17
Weezing Master Trainer: Rocket Hideout
Rhyhorn Master Trainer: Route 17
Rhydon Master Trainer: Rocket Hideout
Chansey Master Trainer: Fuchsia City
Tangela Master Trainer: Route 15
Kangaskhan Master Trainer: Fuchsia City
Horsea Master Trainer: Route 19
Seadra Master Trainer: Route 12
Goldeen Master Trainer: Route 12
Seaking Master Trainer: Route 13
Staryu Master Trainer: Route 19
Starmie Master Trainer: Route 25
Mr. Mime Master Trainer: Celadon City
Scyther Master Trainer: Route 15
Jynx Master Trainer: Cerulean City
Electabuzz Master Trainer: Route 10
Magmar Master Trainer: Pokemon Mansion
Pinsir Master Trainer: Route 18
Tauros Master Trainer: Fuchsia City
Magikarp Master Trainer: Route 4 West
Gyarados Master Trainer: Celadon City
Lapras Master Trainer: Pokemon Tower
Ditto Master Trainer: Pokemon Mansion (4,000+ Combat Power Level)
Eevee Master Trainer: Route 17
Vaporeon Master Trainer: Celadon City
Jolteon Master Trainer: Celadon City
Flareon Master Trainer: Celadon City
Porygon Master Trainer: Celadon City
Omanyte Master Trainer: Mt. Moon
Omastar Master Trainer: Cinnabar Island
Kabuto Master Trainer: Mt. Moon
Kabutops Master Trainer: Pewter City
Aerodactyl Master Trainer: Pewter City
Snorlax Master Trainer: Celadon City
Articuno Master Trainer: Seafoam Islands (7,500+ Combat Power Level)
Zapdos Master Trainer: Power Plant (7,500+ Combat Power Level)
Moltres Master Trainer: Victory Road (7,500+ Combat Power Level)
Dratini Master Trainer: Route 23
Dragonair Master Trainer: Seafoam Islands
Dragonite Master Trainer: Cerulean City
Mewtwo Master Trainer: Pokemon Mansion (9,000+ Combat Power Level)
Mew Master Trainer: Pokemon Mansion (8,000+ Combat Power Level)
Meltan Master Trainer: Pokemon Mansion (4,000+ Combat Power Level)
Melmetal Master Trainer: Pokemon Mansion (8,000+ Combat Power Level)