Ahead of your Pokémon League challenge, you should see what Lillie’s been getting up to. Fly to Iki Town on Melemele Island, then head to Mahalo Trail, behind the ceremonial stage. Follow the trail to the very top, where you’ll emerge at the recently fixed Plank Bridge. There, you’ll find Lillie and her Legendary companion.
Now’s your chance to catch Alola’s Legendary Pokémon! Originally you were forced to capture Solgaleo or Lunala at the Altar of the Sunne/Moone to proceed with the story, but this time their capture is optional. Having them on your side would help you with immensely at the Pokémon League. However you can catch them whenever you want.
Solgaleo, the Sunne Pokémon, has exceptional stats, with HP and Attack as its highest stats. For attacks, it can use Sunsteel Strike, a devastating Steel-type move that ignores Abilities, Zen Headbutt for Psychic-type STAB, Crunch to hurt Ghosts, and Cosmic Power to boost its defensive stats. Its Ability negates stat lowering.
Against this fearsome lion, Dark-types are recommended to inflict damage, then switch over to a Steel-type to resist its STAB attacks. Because you can’t lower its stats, inflicting it with paralysis would be extremely useful. You could also use Battle Items, like Roto Boost, to up your Pokémon’s stats for a potentially drawn out battle.
Lunala, the Moone Pokémon, also has exceptional stats, with HP and Special Attack as it shighest stats. It can use Moongeist Beam, a powerful Ghost-type move that ignores Abilities, Shadow Ball for when Moongeist Beam runs out, Night Daze after Shadow Ball runs out, and Cosmic Power. Its Ability weakens damage when at full HP.
When facing this spooky bat, Dark-types are ideal for resisting its attacks, but you need to be careful when attacking as their attacks do 4x damage. Thankfully Shadow Shield should prevent a one-hit KO. Speaking of, be wary of Shadow Shield when calculating damage, as the first hit you land will be significantly weaker than subsequent hits.
Compared to regular wild Pokémon, the biggest difference is that Legendary Pokémon can hit really, really hard. So bulky Pokémon or Pokémon that resist their STAB moves are essential. On top of that, it can take a lot of Poké Balls to catch Legendary Pokémon, so make sure you have lots ready–especially Ultra Balls.
Other than that, the general strategy is the same: weaken the Legendary Pokémon, then start throwing balls like crazy. Thankfully, both Pokémon do not have access to healing moves, so once you’ve got their HP low enough, you only have to worry about your Pokémon’s HP. If necessary, use Roto Catch if you were lucky to roll one.