Read here how to take on Olivia of the Elite Four!
Elite Four Olivia uses the following Pokémon:
The Swift Swim Ability doubles Relicanth's Speed in rain.
Relicanth tends to use moves that are super-effective against your Pokémon. It may also use Yawn.
Carbink's Clear Body Ability prevents stat reduction.
Carbink tends to use moves that are super-effective against your Pokémon. It may also use Reflect.
Its Sturdy Ability makes Golem survive moves that would otherwise make it faint, with 1 HP if its HP was full. It also makes it immune to one-hit knock-out moves. Moves that hit more than once (like Double Kick) can bypass it.
Golem tends to use moves that are super-effective against your Pokémon.
Probopass has the Sturdy Ability, just like Golem.
Probopass tends to use moves that are super-effective against your Pokémon. It may also use Thunder Wave or Sandstorm.
Its Keen Eye Ability prevents Lycanroc's accuracy from being lowered. With its Rockium Z, a single Stone Edge can turn into the Z-Move Continental Crush which deals lots of damage.
Lycanroc tends to use moves super-effective against your Pokémon. It may also use Counter or Rock Climb, and may use its Z-Move if it cannot knock your Pokémon out otherwise.
Ground is a very useful type as Golem and Probopass are 4x weak to it. Keep in mind that both of them have Sturdy, though, which means most Ground-type moves can’t take them down in one turn. A notable exception to this can be found below. However, even with Sturdy, Ground is a good type for this battle in general, with only Relicanth’s Hydro Pump being a threat to it.
Grass is also useful with Relicanth being 4x weak to it, and it also works well against Carbink and Lycanroc. Golem’s STAB Thunder Punch is resisted, but its Steamroller is super-effective to it, so be careful. Also, Probopass can’t be hit for super-effective damage.
Using Fighting also works. Probopass is 4x weak to it and Double Kick can bypass Sturdy. It only needs to be careful of Carbink and its Moonblast. If you consider Reflect annoying, Brick Break can get rid of it.
Steel is also good, as Carbink is 4x weak to it. Keep in mind that Relicanth doesn’t receive super-effective damage from it, and Probopass’ Earth Power is super-effective against it.
Finally, Water is also useful, hitting Carbink, Probopass, Golem, and Lycanroc for super-effective damage. However, Golem can be a threat too, with Thunder Punch. Relicanth is hit for neutral damage, but its Hydro Pump is resisted.
Relicanth and Golem are much more suspectible to special attacks than physical. Lycanroc and Carbink have the same Defense and Special Defense (in Carbink’s case, both are high), but Reflect makes special a better option for Carbink (and potentially several Pokémon after it as it lasts for 5 turns), and Counter makes it a better option for Lycanroc too. Probopass is slightly more weak on the physical side of the spectrum; both defenses are high, but the fact it has two double weaknesses means it won’t matter much. Special is generally the better option, but do not hesitate to use physical attacks especially against Probopass (as Ground/Fighting have stronger physical moves) and/or all the other cases of 4x weakness.
Alolan Dugtrio combines two viable types (Ground/Steel) and is agood choice during the whole game.
Tsareena is a good Grass-type to use.
Kommo-o is a good Fighting-type, available at its previous forms at a good level (close to its final evolution level requirement) and in an area a bit before the League (Vast Poni Canyon). It has great base stats.
Note that Alolan Marowak is the only easily available Pokémon with access to the Ground-type moves Bonemerang and Bone Rush. Those moves do not receive STAB but they hit more than once, making them the only Ground-type moves bypassing Golem’s and Probopass’ Sturdy. However, Alolan Marowak's Fire-type makes it not a good option for the rest of Olivia’s Pokémon, but with Golem and Probopass having low base Speed it might be able to knock them out in one turn, easily getting rid of two out of five Pokémon that would otherwise be potentially troublesome with their paralysis/Sandstorm moves. Ideally you should’ve kept one of these moves on it while using it throughout the game (for coverage) but if not, you can still teach it by the Move Relearner, conveniently placed in the Pokémon Center outside the Pokémon League, in exchange for a Heart Scale (which you can obtain from restaurants).
As for the starter Pokémon; Decidueye is very good against Relicanth, Carbink and Alolan Golem (Steamroller isn’t super-effective thanks to its Ghost typing), and decent against Probopass. It is immune to Lycanroc’s Counter and Rock Climb, but does have to be careful of Crunch. Incineroar has no particular strengths in this battle, so its teammates will have to help out here. Primarina is very good, just like most special-oriented Water-types, and its Fairy type helps slightly, too.
Relicanth is the first Pokémon that will be sent out; using a Grass-type move against it will likely knock it out before it does anything. If it does stay around though, you should be careful of its Yawn; you may either switch out or deal with the Sleep status condition. If you want to use a rain + Water-type sweep strategy, keep in mind that with Swift Swim and Hydro Pump, it can end up deadly; you may want to knock it out and set up rain on another Pokémon instead.
Carbink is a bit harder to take down because of its high defenses. However, its attacks aren’t very strong, so as long as you are careful about type advantages you won’t have a problem with those. If you don't want it to use Reflect, you can use Steel-type attacks against it (maybe even the Corkscrew Crash Z-Move, as the other Pokémon are defensively weaker). The Clear Body Ability prevents its stats from being lowered, but that wouldn’t be a particularly effective strategy anyway.
For Alolan Golem, Ground-type Pokémon don’t have to worry about paralysis from Thunder Punch, while taking it down with two attacks (because of 4x weakness and Sturdy). The Alolan Marowak strategy is the only easy known way to take it down in one turn (although a Double Kick from a Pokémon that is sufficiently overleveled and with high Attack might do it too).
For Probopass, the Alolan Marowak strategy and Double Kick may be able to take it down in one turn, else, once again, you may want to use two 4x effective attacks. Keep in mind that Ground-type Pokémon are somewhat more viable as they are immune to the potentially disruptive Thunder Wave. If it sets up a Sandstorm, you can either let it be, replace it with other weather, or just stick to Ground/Steel-types that have no problems with it.
Lycanroc, being a pure Rock-type, has lots of weaknesses, but is the only Pokémon in this battle that doesn’t have at least one 4x weakness. If you use physical attacks on it you need to be careful of its Counter. Its Z-Move can also be deadly, but Fighting/Ground/Steel-types at least resist it. Fighting also resists Crunch. In any case, taking it down shouldn’t be too hard, the strategy for it is somewhat straightforward.
Keep in mind that Olivia, like all the Elite Four, uses healing items, particularly when her Pokémon’s HP is low. You may either try to make her Pokémon faint without ever giving her the chance to do so (although the 1 HP situation of Sturdy makes it hard), or let her do it soon so that you won’t have to deal with it later, when she will be using more threatening Pokémon.
Overall, this shouldn’t be too hard of a battle thanks to type advantages, as long as you are careful of a few moves Olivia’s Pokémon have.