Red's Pikachu, despite being the highest levelled Pokemon his team, is actually the easiest to take out. It has two Electric-type moves as well as the priority move Quick Attack and the Attack-reducing Charm. Any strong Ground-type move should be able to defeat it in one blow, and a Pokemon like Golem or Steelix isn't afraid of it at all. Just be careful of a switch into Blastoise or Venusaur, both of which can threaten these Pokemon with their STAB moves. Espeon, the lowest levelled Pokemon in Red's party, can hit hard with Psychic and set up Reflects but is useless otherwise. Steel and Dark-types like Scizor and Tyranitar can repel its moves and hit with their STAB attacks for an instant kill, but need to beware of Mud Slap: the damage is low even with a super-effective boost, but the accuracy drop it guarantees is incredibly annoying. Snorlax likes to come out and use Amnesia to buff its Special Defense, so punish it with a strong Fighting-type move such as Dynamicpunch (if you can get it to land!). It will Rest off damage when its HP gets low then strike with Snore, but it can't heal itself on the turns it's asleep. Watch for Body Slam, which can leave you paralyzed amd hits hard as a STAB move.
The Kanto starters like to use weather moves to buff up their moves and create combos for one another. Venusaur uses Sunny Day to help out its Solarbeam and fully restore HP with Synthesis, while also giving Charizard a bit of a boost in Flamethrower and Fire Spin. Giga Drain is too weak to do any real damage but it'll suck up a bit of health nevertheless, giving Venusaur more longevity. Charizard only has Wing Attack and Slash in its arsenal in addition to its Fire-type attacks, making it susceptible to Rock-types and their STAB attacks. Blastoise will summon a rain storm with Rain Dance, making Surf and Whirlpool a bit stronger and giving Pikachu's Thunder perfect accuracy. Kingdra is recommended for all three starters as it resists most of their moves and takes advantage of the rain to hit hard and heavy with Hydro Pump or Surf. If you manage to beat all six Pokemon, congratulations! You have now beaten the strongest trainer in Gold and Silver and will get to watch the credits roll.