Current team:
Picture taken right after finishing Mount Lanakila.
Here's how all the major battles went:
Fairy Trial:
For this trial, Mina tasks you to to talk to the past Trial Captains, fight them, and claim a colored petal from each of them. At first, I had trouble finding Ilima, but then I talked to Mina again after she initiated the trial, and she mentioned to go to Route 2 first and talk to the Trial Guides, for they will give pointers to where the Trial Captains currently are. The Trial Guide at Route 2 then told me to go to Hau'oli Cementary to find Ilima. Sure enough, he was there, and I had to battle him. Battle was pretty easy. Not much to say. He then took me to Lush Jungle, where Mallow and Lana were waiting for. You can choose which of the two you want to fight, and they'll both give you their petals. They then take you to Kiawe's location, you fight Kiawe, and then he gives you the petal. He takes you to Hokulani Observatory, and the process repeats itself with Sophocles. Sophocles then takes you to the Aether House where Acerola is waiting, but Nanu is there instead and he gives you the petal automatically without having to fight you. You then head back to Mina's house so that she makes the flower, and then Totem Ribombee is summoned.
Let me put it this way: A Steel-type Pokemon is your best bet against Ribombee. Fire-types are not a good idea at all. Why? One of its Ally Pokemon it can summon is Pelipper...
with Drizzle. Yep, forget about using Fire-types. Also, Ribombee can summon Blissey as its Ally Pokemon. That Blissey knows Heal Pulse, and it will use the same strategy of healing Ribombee using it just like Alolomola did with Totem Wishiwashi in Sun/Moon. Totem Ribombee also knows Quiver Dance, which is devastating when combined with its Z-powered stats.
Luckily for me, this battle was over in a turn, but that was because I was rather overleveled and had a Steel-type. Ribombee managed to outpaced Mikasa and deliver a very powerful Bug Buzz to it that Mikasa still managed to survive, but one Iron Head was all that it took to take it out.
Grand Trial vs Hapu:
Largely the same battle from Sun/Moon, except now a Golurk replaces her Alolan Dugtrio and the battle takes place on Exeggutor Island instead of the entrance to Vast Poni Canyon.
I was still quite over leveled, so Makoto managed to knock out three of her Pokemon quite easily. Rem took care of the Gastrodon at the end.
3rd Battle vs Gladion:
Same battle from Sun/Moon, except Zoroark replaces his Weavile.
Seems like leading with Siegfried thinking that its higher level would do well against a lower leveled Crobat wasn't the best option, as Siegfried went down to a single Acrobatics attack in one go. Mikasa had to intervene with a Stone Edge to finish Crobat off. Silvally was able to have an answer to Rem, so I switched into Sirius to finish the job. Next came his Zoroark, which I thought was his Lucario because of the Illusion ability. It became clear it was Zoroark when it used Night Daze. Luckily, one Flamethrower took out Zoroark quite nicely. Last but not least was Gladion's Lucario, and Siegfried took care of it with a single Close Combat. A fun fight, if I do say so myself!
Catching Necrozma and Solgaleo:
Both only took one Quick Ball and that was it. They really lowered Necrozma's catch rate from the last game.
Story updates:
For what it was worth, the Fairy Trial was a nostalgic ride by revisiting the past Trial Captains. When arriving at Hau'oli Cementary, Hau runs into with his now fully evolved starter and mentions he has been doing a lot of training to prepare for a big battle against you. Several of the Trial Captains allude to Hau, noting how he has been doing some extensive training in Mahalo Trial and even managed to beat his grandfather in an all-out battle to prepare for his greatest battle yet.
I had a chuckle with Lana and Mallow's peace as they mentioned "Don't you want to be accompanied by some pretty girls on your way to meet Kiawe," and when we meet Kiawe again, we learn that he has plans on making the photo-bombing Hiker the next Trial Captain. At Hokulani Observatory, we see Molayne parting ways with Sophocles, who is rather upset about it, but he decides to stay to watch the battle between you and Sophocles.
When you arrive at the Aether House to meet Acerola again, Guzma is waiting outside. He apologizes for all that happened prior, and Hau shows up. Hau brings up how everyone in Team Skull looks up to Guzma for his strength as a trainer. Guzma also reveals that his Golisopod was his first Pokemon, which he met when it was only a Wimpod, and this was long before he started doing the Island Trials. Not much of a surprise since many head cannons imagined little Guzma with a Wimpod, but hey, nice to have official confirmation! Guzma gives you the Grip Claw before leaving.
When you enter Aether House, Acerola isn't there, but you witness a cute scene where Nanu is teaching the little kids how to do the Dark-type Z-move pose.
After beating Totem Ribombee, Hala is seen talking with Hapu before you are told to go to Exeguttor Island. I guess he was giving Hapu some advice regarding Kahuna lifestyles now that she finally became one herself.
After fighting Gladion, Gladion does not state how Lillie sees you as the best trainer in the world. Instead, he mentions that her and Nebby are waiting at Mahalo Trail. When you get back there, you see Nebby and her at the front of the bridge. She tells you that Necrozma needs to be near Nebby in order for it to ease its pain, hence why she wants you to catch Debby. Thus, Mahalo Trail is where you can catch Solgaleo/Lunala in USUM. After catching the legendary, Lillie's dialogue following the scene is basically the same from Sun/Moon at the conclusion of the Altar events.
I then went back to Ten Carat Hill to get the Flynium-Z. Upon getting it, Kahili randomly shows up without introducing herself just yo show you how to use its Z-move. Okay...
Now Mount Lanakila was where things get interesting. One major change that I really liked about it is that there are now multiple trainers present throughout it. This makes the mountain feel like an actual Victory Road like it was supposed to be. In the Sun/Moon games, it felt lacking not to run into trainers on the way up to the Pokemon League, so I'm glad they fixed it. It is also in Mount Lanakila where you find the TM for Poison Jab now.
They changed up the layout in some parts of the mountain too. There's a point where you go temporarily outside to fight two double battles against a few Black Belts. After that, you run into a crater where Necrozma is waiting. It is there where you can catch it, but you do have the option of avoiding it since there is a path to the right. When you catch Necrozma, Colress shows up to tell you about the devices he was creating: the N-Solarizer and the N-Lunarizer, the two items that allow Necrozma to transform into Dusk Mane/Dawn Wings forms respectively. You also get the UltraNecrozmium Z upon catching Necrozma.
When you finally reach the summit of the mountain, Hau does not show up to challenge you to one final battle. Kukui is still present at the entrance to give you his brief speech about his past Pokemon League experience and how he looks forward to seeing how you will approach the League, but once he leaves, a heart-warming scene takes place.
Your starter suddenly comes out of its Pokeball, and you two have a cute little exchange. You are then treated to this:
You and your starter Pokemon reflect on the memories leading up to this point as the two of you face the Pokemon League entrance. Sadly, there are no flashbacks in this scene, but it was still nice scene nonetheless.
Time to challenge the Elite Four!