Elite Four: Lorelei
Specialty: Water & Ice-type

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The first member of the Elite Four, Lorelei, has an excellent team to start off against. Although she says freezing moves are powerful, only two of her Pokemon can freeze you. Don't think you're off the hook though; when frozen in Generation I, you will never defrost unless hit by a Fire-type move, and unfortunately for you none of her Pokemon carry one. Her leading Pokemon, Dewgong, will use Rest to heal off all damage, so try and take it out quickly or during the turns it's asleep. The move Thunderbolt is excellent for that, and even moreso on a Lapras who can essentially wall her entire team. Slowbro needs to be dispatched extremely quickly as well as Amnesia is frightening: it boosts the Special stat by two. Cloyster has ludicrous Defense and will trap you with Clamp the way Blaine did with Fire Spin. Jynx isn't as bad as the rest of the team if you use strong Rock-type moves, but watch out for a mean Ice Punch from her should you break out a Golem or Onix. Her Lapras is also a terrifying with its Confuse Ray and Blizzard combo - your own Lapras would be the best counter.

Elite Four: Bruno
Specialty: Rock & Fighting-type

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Undeniably the easiest trainer in this challenge, Bruno is still a force to be reckoned with. His team is very akin to Brock and the Fighting Dojo master's teams, using Onix as well as the Hitmons as main staples. His Onix share the exact same movepool; if you finish one off you'll have no problem with the other. Hitmonchan's moveset is practically useless save for Counter, which can totally destroy you if you're taking the route of powerful Flying-type moves on the Fighting-types. Hitmonlee has Jump Kick and Hi Jump Kick, both extremely powerful attacks. A recommended strategy is to use Fly on it with something; if it tries to Jump Kick or Hi Jump Kick you in the turn you're in the air, it will miss and take bad damage from it, setting up for a guaranteed KO the next turn with Fly. Machamp is the only true threat here as it has a great moveset which includes the OHKO move Giovanni gave you. If you have something impervious to ground you'll have no troubles though. A Gengar works wonders here as it avoids all Fighting/Flying moves and strikes back with a buffed-up Psychic.

Elite Four: Agatha
Specialty: Poison & Ghost-type

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This old bird makes great use of the Gastly lines, stuffing her team with two Gengars and a Haunter. This generation has an issue with the type match ups - because of that, Psychics are impervious to Ghost-type moves. A good Pokemon here would be Alakazam, who can sweep the entire team with just Psychic and will have the speed to beat out Gengar and Golbat. As long as you don't get hit by physical attacks you'll be golden. This team loves status moves, with everything being able to do almost anything under the sun, including poison, sleep, confusion, and paralysis. Don't afford them any of those luxuries - confusion will ruin a physical sweeper if it hits itself, sleep will leave you susceptible to Dream Eater (which most of the team save for the non-Ghosts runs), paralysis will lower your much needed Speed, and poison is, well, poison. Ground-type moves are great here too because the Gastly line doesn't have Levitate in this generation, leaving four fifths of the team open to a strong Earthquake or Dig. Don't bother with Normal or Fighting-type moves here though because they'll be useless on the Ghosts. If you are put asleep at any point, remember you can save healing items by using the Poke Flute to awaken.

Elite Four: Lance
Specialty: Dragon-type

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The king of the Elite Four, Lance, has the most frightening team of all. Gyarados, his lead, has decent Special in this generation and can wipe you out with Hydro Pump or Hyper Beam depending on what works better. Hyper Beam, by the way, is a staple of his team, and has an interesting quirk - if it knocks a Pokemon out it won't need to recharge. Luckily Gyarados has a double weakness to Electric-type moves, so hit it with those for maximum punishment. His two Dragonairs share a moveset that includes Dragon Rage (a set 40 damage move), Agility, Slam, and Hyper Beam. Dispose of them quickly or use a Rock-type with great Defense to sponge their moves and whittle them down. Rhydon or Golem works wonders here, as does an Omastar with Ice Beam. Aerodactyl is fast and has great Attack but poor moves - in fact, a Gengar can wall it completely. The main attraction, Dragonite, can set up a Barrier to boost Defense then take you out with a Hyper Beam backed by one of the highest Attack stats in the game. It does have a double Ice weakness though - exploit it.

Elite Four: Rival
Specialty: None

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The circle is now complete. Your first and last challenge is with your rival, and he'll have just as many tricks as ever to face you. With a fully rounded out team you'll be hard pressed to find one Pokemon to take everything out; however, if you don't mind legendaries, I recommend Zapdos for its Electric-type (good for beating literally up to 2/3 of the team depending on who he chose, or at the very least half) and Flying-type (provides STAB and good speed to take out Alakazam with a quick physical move). If not, balance everything out as always: don't train just one Pokemon (seriously don't) and make sure your type coverage is astute. Decibel dmg cracked for mac free. His team has a few flaws you can exploit: Arcanine, if he has it, laughably knows Ember as its Fire-type attack, Gyarados's Hyper Beam makes it stall a turn if it doesn't wipe you out, Exeggutor only has three attacks (both damage-inflicting ones of the Normal-type), and Rhydon has a low-accuracy OHKO move it'll try on you. An alternate approach to this is to just use Toxic on everything (use PP Up if you're doing this) and stall it out with Chansey or another bulky Pokemon. It's not exactly enthralling but if it's what works go for it. Good luck!