Chapter 7: Mossdeep Gym
Travel east out of Fortree City and travel along Route 120 until you reach Route 121. Continue along to find Team Aqua. Now go south of where Team Aqua was to find Route 122. Use Surf to travel south and head east to find a cave. Enter it to find Mt. Pyre. Continue to the top of Mt. Pyre to find Team Aqua. Continue along by fighting the Team Aqua members.
At the top of Mt. Pyre will be a dialog with Team Aqua leaders. Now you must battle with Matt from Team Aqua. A dialog happens once more after the battle. You will be given the Red Orb. Now head to Slateport City and head to the northeast part of town for a short dialog. Now follow Stern inside the building for another dialog. Fight both Team Aqua Grunts and agree to help Stern.
Once in Lilycove City - a short dialog will ensue. Afterwards, exit the Lilycove City Harbor and head north into town. Continue north to find Brendan/May, who will battle you. Defeat him and continue north. Now head east and jump down the small ledges. Go south until and down the stairs. Head east and north to find a cave. Use Surf to enter it - this is the Team Aqua Hideout.
Team Aqua/Magma Hideout
This Team Aqua Hideout guide is only applicable to Alpha Sapphire version.
Head north and continue up the stairs to enter the hideout. Take the portal to the east. Now travel through the stairs to the west. Continue west through the portal. Go east and up the trail north. Go through the portal. Go east through the portal. Travel east until you reach Team Aqua. A short dialog will ensue and a battle with Team Aqua Grunts happens.
Continue traveling around the area to find a short dialog with Aqua Admin Matt. Continue towards him for another dialog and a battle. After the battle - a short dialog happens and now head north. Go west and through the portal. Head south and exit the Team Aqua Hideout. Head east across the water to find Route 124. Continue east along Route 124 until you reach Mossdeep City.
Go to the Mossdeep Gym and continue north. Battle the first trainer and hit the switch. Go south and now back north. Battle the trainer and hit the switch. Head east, fight the trainer, and hit the switch. Take the southwestern path, fight the trainer, and hit the switch. Take the southwestern path and continue south. Head north to find the Mossdeep Gym Leaders.
Gym #7 Mossdeep Gym - Leaders Tate & Liza
Mossdeep Gym is unique in that it has two Gym Leader, Tate and Liza, that work together in a double battle using their Psychic-type Pokémon. The gym's puzzle is quite easy, you'll just need to step on switches that open up new pathways that will eventually lead you to the Gym Leaders. Liza and Tate's Psychic and Rock duo can make Mossdeep one of the most difficult Gyms to defeat; but they do have weaknesses of Water, Ghost, and Grass types. Watch out for the variety of move types (Fire, Rock, and Grass) that might be unexpected from Solrock. Focusing on one of the two before the other should make this battle more manageable.
After defeating the Leader duo, you'll get the Mind Badge and TM04 - Calm Mind for your efforts. You'll now be able to use Dive outside of battle and rely on Pokémon up to Level 80.