Talk to the Game Director inside the Celadon Mansion in Celadon City to receive the Diploma after catching all 150 Pokemon (not including Mew)
Bonus: Capture Mew - Event Pokemon not currently available through standard gameplay. Mew may be glitched into the game by following these instructions: bit.ly/RedBlueMewGlitch. This also appears to work in the 3DS Virtual Console.
Collectibles and Gifts
Obtain all TMs - see this checklist: https://bit.ly/RedBlueYellowTMs
Obtain all In-Game Gift Pokemon
Magikarp - Sold by the Magikarp salesman in the Route 4 Pokemon Center for ₽500.
Omanyte/Kabuto - Retrieve the Helix or Dome Fossil from Mt. Moon and have it revived on Cinnabar Island. Only one fossil per game file.
Aerodactyl - Retrieve the Old Amber from the Pewter Museum of Science and have it revived on Cinnabar Island.
Hitmonlee/Hitmonchan - Given after defeating the Karate Master in the Saffron City Fighting Dojo. Only one Pokemon given per game file.
Eevee - Given by a man on the Celadon Mansion rooftop in Celadon City. Enter in the back door.
Lapras - Given by a Silph. Co Employee in the Silph Co. Headquarters 7F after defeating Blue
Complete all In-Game Trades
Trade an Abra to a boy on Route 2 outside of Diglett\'s Cave to receive a Mr. Mime
Trade a Nidoran (male) to a girl in the Route 5 Underground Tunnel North Exit to receive a Nidoran (female)
Trade a Nidorino to a man upstairs in the Route 11 Guardhouse to receive a Nidorina
Trade a Slowbro to the man upstairs in the Route 18 Guardhouse to receive a Lickitung
Trade a Poliwhirl to the elderly man in the house next to the Pokemon Center in Cerulean City to receive Jynx
Trade a Spearow to the woman in the house east of the Pokemon Center in Vermillion City to receive a Farfetch\'d
Trade a Ponyta to a Scientist in the Cinnabar Island Laboratory to receive a Seel
Trade a Raichu to an old man in the Cinnabar Island Laboratory to receive an Electrode
Trade a Venonat to a girl in the Cinnabar Island Laboratory to receive a Tangela