Team Galactic Headquarters
Travel to Veilstone City where you'll find Team Galactic's headquarters. They have captured some Pokemon and you have to free them. You start in the lower levels, searching for the galactic key that unlocks the tower. Here, you have to battle more trainers and the boss Cyrus and Commander Saturn. Cyrus flees after you win these battles, while you get a Master Ball and Team Galactic releases the enslaved Pokemon. In the headquarters you can also find several TMs and potions.
Mt. Coronet
Mt. Coronet is a place you will have visited before, and you need to go back again to explore areas you could not reach earlier. Follow the path up the mountain, collecting items and battling trainers along the way. The battles aren't difficult, and the sheer number of trainers will slowly drain your Pokemon's health, but chances to heal are plenty. At the end of the path, you have to battle Commanders Mars and Jupiter. When you beat them, you'll find Cyrus, who will throw you into the Distortion World.
Distortion World
This area change the physics of the world around you. You can walk on walls and ceilings. You need to cross platforms, chasing Cyrus as you look for the center of the Distortion World. When you catch up with Cyrus, you will have to battle him once again. Defeating him leads to a battle against the legendary Pokemon Giratina. Defeating this Pokemon will free you from the Distortion World so you can continue your journey.
Sunyshore City
With all the side quests complete, make your way to Route 222 -- the path to Sunyshore City, which is home to the final gym, and Gym Leader Volkner, who holds the Beacon Badge. Route 222 is a simple path with trainers and items to collect. When you get to Sunyshore City, talk to Volkner at the lighthouse to send him back to his gym. Follow him there, battle with the trainers and Volkner himself, and collect the last badge you need to enter the Pokemon League.