Fly to the Pokémon League's upper half and, after descending the waterfall, enter Victory Road from there. Use Rock Climb to go down and head for the nearby stairs you saw earlier. Now that you are Champion and have the National Pokédex, the door in the eastern side of this area is no longer blocked off.
When you arrive, clear the fog. You'll quickly encounter a girl named Marley who would like an escort through the tunnel. Just like the other Multi Battle partners, she'll completely heal your team after each battle.
This area is a maze and as long as Marley is with you, you cannot use Surf as a means of creating a shortcut. From where you first met her, use Strength on the nearby boulder and go north. Continue traveling north, carefully moving boulders out of the way, while defeating Trainers. Getting both items in the northwestern part of the room requires two separate trips due to a boulder puzzle.
Now, travel east and continue moving boulders. Once you reach the end of the path, travel south and follow the path east. Once you get past two more Trainers, you'll find the exit and Marley will leave you. Before leaving, Surf around to pick up the items that were inaccessible before. Also, Ace Trainers Arthur and Clarice are located in the southeastern area of the room and can only be accessed after Marley has left. When ready, follow the path to the exit to enter Route 224.
If you need to return to the Pokémon League at any time to heal your team, the good news is that you won't need Strength to navigate through Victory Road B1F again, as Surf alone will make it easy to come and go from Route 224.
The Trainers on this route, much like the ones you just dealt with in Victory Road, have diverse teams and can be tricky to defeat unless you are prepared. There are also some maze-like areas around this route that require a little navigation. You will need Surf to access the Berry patch on this route and to collect some of the items. Other than that, this should be a straightforward route.
Once in Snowpoint City, talk to the Sailor to board the ship to the Battle Zone. You can also visit the Snowpoint Temple if you want, but that will be covered later in this walkthrough.
Before you go, Cynthia will appear and give you a pep talk about how people must work together to help change the world so no one ends up like Cyrus. She wants you to go the Battle Zone to learn and grow. After you speak with her, the ship will depart for the Fight Area.
When you arrive, Barry will be there and drag you to the front of the Battle Frontier. It turns out that Flint and Volkner are preventing him from entering, believing he may not be strong enough. Once you accept Barry's offer for a Multi Battle, the two of you will automatically engage the Trainers in a double battle. You can still reject the offer if you need to prepare your team.
After the two leave, you'll meet Barry's father Palmer, one of the Frontier Brains. He'll explain how each facility has its own rules before he leaves. Barry explains that his father is the reason he decided to become a Trainer. You'll then meet a boy named Buck who was impressed with your recent battle. He that mentions he usually trains at the Survival Area or Stark Mountain.
Go near the Fight Area's north exit to talk to a Fisherman who will give you the Super Rod, the best fishing rod in the game, which will help you obtain some non-regional Water-type Pokémon. After that, go north to Route 225. (You will need the HMs Cut, Surf, and Rock Climb.)