This is part of the A Legendary Tree of a Legendary Three! quest.
After disturbing the Legendary birds at Dyna Tree Hill, Galarian Moltres will decide to take a vacation at the Isle of Armor. As far as we can tell, Moltres does a anti-clockwise loop of the island. If it’s nearby, you can hear its cry when you enter or re-enter the area.
Similar to Articuno, rather than taking the taxi to random areas of the island, we suggest sticking to one place (i.e. keep flying to the same location). The easiest spot seems to be near the Master Dojo (at the Fields of Honor). When you arrive, run towards the road and face the sea.
If Moltres spawns close by, all you have to do is get in front of it. Hopefully, Moltres will notice you and stop mid-flight, with an exclamation mark above its head. After a brief while, it’ll then attack you. However, if you don’t get in front, Moltres will fly faster than you can bike, so don’t bother chasing it.
Like Articuno, Galarian Moltres went from zero to (relative) hero. With its Dark/Flying typing, Moltres is weak to Electric, Rock, Ice and Fairy. In terms of attacks, it can unleash Fiery Wrath, which can cause flinch, Hurricane, Sucker Punch and Nasty Plot. When an attack lowers it HP below 50%, its Sp. Attack will go up.
We recommend having a Fairy-type take the brunt of Moltres’s attacks. A Dark-type could also work. Like Articuno, you’ll want to be mindful of Hurricane, but it only has 5 charges and will probably miss some of them. If you want to be extra careful, Klefki is a Steel-type on top of being Fairy, so it’ll resist all of Moltres’s moves. Sword players have an even better option in Zacian.
Since this battle can last a while (with you chipping Moltres’s HP and chucking Poké Balls), be wary of Moltres’s boosted Special Attack–primarily from Nasty Plot, but also from Berserk. This can cause even its resisted moves to hurt and, for most Fairy and Dark-types, turn Hurricane into a major threat.
A Pokémon that can lower Moltres’s stats or cancel its stat boosts might be useful here. Galarian Weezing is a Fairy-type that can learn Haze (which cancels stat boosts). You could catch one wandering around (eg. at East Lake Axewell) and give it some candy to get it up to speed.
Besides that, you should know what to do. Lower its HP as much as you can, cripple it with paralysis etc., then get into position to unleash a barrage of your best Poké Balls. Hmm, but its colour does suit Luxury Balls… (No, don’t do this unless you’re really persistent!)