From Bulbapedia, the community-driven Pokémon encyclopedia.
Putting Out The Blaze
Once you reach Curl Bay, there is a Munchlax on the east, catch it. Then go north. There will be a cutscene in which the pinchers form Rasp Cavern are attacked by Raikou and they take their anger out on you. Get ready to catch a Piplup and an Eevee. The Raikou's cry drives the Pinchers away.
Now go down the stairs on the east and break that rock with the help of Munchlax. Then catch that Shellos. Finally get that Buizel and the other Buizel on the top.
Once you get to Rand's House, you find that the house is on fire. Quickly put it out, you need a Pokémon with Soak 1. The nearby Totodile is perfect. Use it to put out the fire. Then a Huge Fire bursts out and the Team Target Clear Tutorial is activated. Now use the Shellos and Buizel you caught earlier to put the Huge Fire out.
Inside the house, Nema fixes your Styler and the Styler Modification Tutorial commences. Then get out and throught the east exit.
On Latolato Trail, go west then north.
Mt. Latolato is basically a single path. If you noticed a Bonsly, use Soak 1 on it to make it come up. There will be a pincher waiting for you with an Ivysaur. So be ready. After passing a Tyrogue, you see some rocks. They are actually Graveler.
When you get on the bridge a pincher will come with a Wobbuffet. Catch it.
When you get up to the Wireless Tower, you have to battle an Aipom, a Skuntank and a Gligar together. Use Poké Assists and loop away to victory.
Liberate the Wireless Tower
After the coversation, get out of the shack and get in the Wireless Tower and the agitated Pokémon tutorial begins.
Then go north then west and catch the Gligar. Then head back east and cut that Barricade. Then go north then west and you see some pinchers. Get ready to catch an angry Pichu. Then go up the stairs.
The yellow path will have current flowing periodically, so try not to get shocked. Go north, then go east, then south and catch a Gligar. Then north, west and then cut the Barricade and proceed north. Catch the agitated Voltorb and then go up the stairs.
Go west and open the Gate with an Electrify 1 from Voltorb. Go south and 3 pinchers are waiting for you with a Lairon and two Aron. The Lairon is agitated. They run off after the capture. Continue up the stairs.
On this floor, there will be strong winds which continously push you in one direction. If you fall off the platform you will end up here. Go south then east through the yellow path. Then go north, east and south to reach the stairs.
Go west and you see Raikou chasing the pinchers. Go north and get a Hitmonchan and go south then west and catch this one too. Use them to destroy the Huge Block to the east. Now one thing to remember is that you should catch as many Gligar as you can because you are going to need them.
Proceed and you see a conversation between some pinchers. Then Raikou appears and destroys the antenna. Then you get to catch Raikou. Use Ground type Poké Assists to make it easy. It's your second boss capture and it has its rage gauge full, so use Poké Assists as much as possible. The Gligar you caught may be useful here.
After the capture you will be prompted to register the symbol you see. Its Mission Clear. After you get down, you see that Burkhart has caught 2 pinchers, after a while they run away. So chase them.
In Pursuit of the Pinchers
Go bach the way you came, till Latolato Trail, where you see them. Then go the way they went. To Hinder Cape. Basically its a single path from here. When you get on the bridge, Red Eyes comes and informs you that Summer/Ben is safe and then destroys the bridge.