Defeat your Rival Red in Oak's Lab
Defeat your Rival Red on Route 22 before traveling to Pewter City
Defeat Brock and earn Boulder Badge in Pewter City Gym
Buy Magikarp on Route 4 (inside of the Pokecenter)
Defeat your Rival Red in Cerulean City
Defeat Bill on Route 25 (inside of the Sea Cottage House)
Defeat Misty and earn Cascade Badge in Cerulean City Gym
Defeat your Rival Red in S.S. Anne Ship
Defeat Captain in S.S. Anne Ship
Defeat Lt. Surge and earn Thunder Badge in Vermilion City Gym
Defeat your Rival Red in Lavender City (inside of the Pokemon Tower)
Defeat Giovanni in Celadon City (inside of the Rocket Game Corner House)
Defeat Erika and earn Rainbow Badge in Caledon City Gym
Defeat Mr. Fuji in Lavender City (inside of the Pokemon Tower)
Capture Snorlax on Route 12 or Route 16
Defeat Warden in Fuchsia City (inside of the Warden's House or Safari Zone House)
Defeat Koga and earn Soul Badge in Fuchsia City Gym
Capture Mewtwo in Cerulean Cave (see comments)
Capture Zapdos in Power Plant
Capture Articuno in Seafoam Islands
Defeat your Rival Red in Saffron City (inside of the Silph Co. Tower)
Defeat Giovanni in Saffron City (inside of the Silph Co. Tower)
Defeat Sabrina and earn Marsh Badge in Saffron City Gym
Defeat Blaine and earn Volcano Badge in Cinnabar Island Gym
Capture Moltres in Mt. Ember (Island 1)
Rescue Lostelle in Berry Forest (Island 3)
Defeat Giovanni and earn Earth Badge in Viridian City Gym
Defeat your Rival Red on Route 22 before traveling to Pokemon League
Defeat Lorelei at the Pokemon League
Defeat Bruno at the Pokemon League
Defeat Agatha at the Pokemon League
Defeat Lance at the Pokemon League
Defeat your Rival Red at the Pokemon League
Help Lorelei and defeat Team Rocket in Icefall Cave (Island 4)
Rescue Selphy in Lost Cave (Island 5)
Capture Entei in Monean Chamber (Island 7)
Capture Raikou in Dilford Chamber (Island 7)
Capture Suicune in Rixy Chamber (Island 7)
Defeat Gideon in Warehouse (Island 5)
Defeat Prof. Oak on Island 7
Defeat Rematch Lorelei at the Pokemon League
Defeat Rematch at the Pokemon League
Defeat Rematch Agatha at the Pokemon League
Defeat Rematch Lance at the Pokemon League
Defeat your Rematch Rival Red at the Pokemon League
Defeat Red and Green in Pallet Town
Capture Mew in Birth Island
Defeat Captain in Navel Rock
Capture Ho-oh in Navel Rock
Capture Lugia in Navel Rock
Catch all 253 obtainable Pokemon and open your Pokedex (see comments)
Defeat Bill in Berry Forest (Island 3) (see comment)
Capture Celebi in Berry Forest (Island 3)
Defeat May in Berry Forest (Island 3) (see comment)
Defeat Brendan in Berry Forest (Island 3) (see comment)