After you get the Mine Badge from the Canalave Gym, Professor Rowan asks you to visit Lake Valor, where an unexplained explosion occurred.
Reach the Lake
You can reach Lake Valor by either going south from Veilstone City or by going east from Pastoria City.
Explore the Area
Go west from the Lake Valor entrance and make your way down the stairs. You eventually have to battle a Team Galactic Grunt who has a level 33 Glameow and a level 33 Croagunk. You get 1584 Pokédollars for winning.
Go west, then north, then west again, and there is a hidden HP Up south of the large group of Magikarps.
Go back the way you came until you can go south up some stairs. Southwest of the stairs, you can battle a Team Galactic Grunt who has a level 32 Golbat and a level 36 Croagunk. You get 1728 Pokédollars for winning.
East of that grunt, you can battle a Team Galactic Grunt who has a level 34 Croagunk, a level 31 Dustox, and a level 31 Beautifly. You get 1488 Pokédollars for winning.
Go east and enter the cave.
Go north and talk to the person to battle Commander Saturn, who has a level 35 Kadabra, a level 37 Toxicroak, and a level 35 Bronzor. You get 3256 Pokédollars for winning.
Go to Lake Verity
Go outside and use the Town Map to fly to Twinleaf Town. Go north from the town, then go west, then north into the Lake Verity area.
When you go north from Professor Rowan, you will have to battle two Team Galactic Grunts. They have a level 32 Silcoon, a level 33 Glameow, a level 32 Stunky, two level 32 Glameows, and a level 32 Golbat. You get 3072 Pokédollars for winning.
Go north from there and there are two Ace Trainers. You can either battle them separately talking to them from below, or battle them at the same time by walking between them.
The Team Galactic Grunt on the left has a level 32 Stunky and a level 32 Glameow. You get 1536 Pokédollars for winning.
The Team Galactic Grunt on the right has a level 31 Beautifly and a level 33 Glameow. You get 1584 Pokédollars for winning.
Go north and talk to the Team Galactic person that Lucas is facing. You will battle Commander Mars, who has a level 37 Golbat, a level 37 Bronzor, and a level 39 Purugly. You get 3276 Pokédollars for winning.
Get the Strength TM
Before you proceed, you should get TM096 Strength. If you don't have it, use the map to go to Solaceon Town, then go south to the Lost Tower, where you can get TM096 Strength.
Check Lake Acuity
After you get the Strength TM (see above), use the map to fly to Celestic Town, heal up at the Pokémon Center, then go west to Route 211.
Near the start of Route 211, there are berry trees.
In the northern part of the area, you can optionally battle Bird Keeper Katherine, who has a level 31 Noctowl. You get 1364 Pokédollars for winning.
To the south, you can talk to the Ace Trainer to get 3 TM77s, which teach Psych Up.
Northwest of the Ace Trainer, you can battle Ruin Maniac Harry, who has a level 30 Bronzor. You get 1680 Pokédollars for winning.
Northwest of the Ruin Maniac, you can approach the mound of dirt to battle Ninja Boy Nick, who has a level 27 Skorupi and a level 27 Golbat. You get 432 Pokédollars for winning.
There is grass to the south. In the grass, you can catch Chingling, Graveler, Machoke, Meditite, and Ponyta. At night, you can also catch Noctowl and Zubat there.
South of the grass, you can battle Black Belt Sean, who has a level 28 Croagunk, a level 27 Meditite, and a level 29 Machoke. You get 928 Pokédollars for winning.
Go west to enter Mount Coronet.