From here on out, Mt. Coronet is an enormous maze. You may want to use Super Repels in some areas, but the wild Pokémon are high-leveled enough to be good for training against. It would be a good idea to keep the Dowsing Machine app on the Pokétch screen, as there will be a lot of hidden items.
Anyway, the exit in the southwestern corner of the room leads to a dead-end ledge on Route 207, where you can pick up a previously-unreachable Iron and Timer Ball. Back inside the mountain, don't forget to pick up TM80 (Rock Slide), as the move it contains is very useful.
Once you reach the northern exit, Looker will show up. Knowing that both Cyrus and the Galactic Commanders are out of his league to fight, he'll let you go on ahead since you're the only one powerful enough to take them on. He will give you the Black Flute before you go. After that, go through the exit and you'll be in 3F.
When you arrive head to the set of stairs on the right to briefly return to 2F to find a hidden Star Piece. You'll also deal with your first two Galactic Grunts, who shouldn't be that much of a challenge if you use the right Pokémon. Afterwards, take the exit to the outdoors, and you'll find yourself in the summit area of Mt. Coronet!
You are now in the southern area of the summit. As it is constantly hailing here, non-Ice-types will receive damage in battle, though you can easily use Super Repels to prevent battles. Also, this area is full of hidden items. From where you are, head east and then north to the Rock Climb-able wall. Near the large patch of grass is the western entrance to 4F, and near another scalable wall is the eastern entrance. Climb that wall and you'll find a grassy area with some hidden items. The eastern 4F entrance serves little purpose at this point, although there are a couple of hidden items worth picking up.
Back outside in the summit, make your way to the northwestern entrance to 4F, in the large grass patch.
Once inside from the west entrance, use Rock Climb to ascend to the upper area of 4F and head for the exit to the east, defeating two more Galactic grunts standing in your way.
Once through the exit from 4F, follow the path and take the stairs down and you will find a narrow chasm with two more Rock Climb walls and another cave entrance that will take you to a special tunnel.
You don't have to explore this part of the cave yet if you don't want to. You can battle three Galactic Grunts and find some hidden items in here. Also, a fourth grunt is guarding the entrance to a secret passage that leads to Mt. Coronet North Side's 1F. You can't go through here until you've stopped Team Galactic for good.
This time, ascend using the Rock Climb wall facing west and follow that path west. This will lead you to the entrance to 5F. Once again, there are some hidden items along the way.
Half of his team that will fight alongside you are determined by which starter he picked at the beginning of the game, but naturally all of them excluding Munchlax have evolved all the way to their final forms.
After the battle, Barry heals your Pokémon before leaving. You'll watch as Cyrus uses the Red Chain to summon both Dialga and Palkia in preparation to destroy the world, then recreate it in his image. Uxie, Mesprit, and Azelf then appear. While Cyrus says it's pointless since the Lake guardians can't match his power, the ground opens up! Another mysterious Pokémon has appeared. Cyrus finds this amusing and then all of a sudden both he and the Pokémon disappear, leaving a portal behind.
Cynthia then arrives and you'll both watch as the three Lake guardians enter the portal. She then reveals that the mysterious Pokémon is Giratina and according to legends, it lives in a mysterious Distortion World. The portal connects to it, and if it isn't closed, it will spread and consume the whole world. Once you accept Cynthia's offer, both of you will head to the Distortion World. Also, at this point both Dialga and Palkia are counted as seen in your Pokédex.