Master Ball and Silver Wing
After you earn the Rising Badge in Blackthorn City, fly to New Bark Town and go to Professor Elm's lab. Talk to Professor Elm to get the Master Ball. This special ball catches any Pokemon without fail, so save it for a hard-to-catch legendary Pokemon. With your new Master Ball in hand, head to Ecruteak City and visit the dance hall. Battle and defeat five kimono girls inside. The last kimono girl gives you the Tidal Bell, an item used to summon Lugia at the Whirl Islands.
Catch or Defeat Lugia
Once you obtain the Tidal Bell, you need to defeat or capture Lugia before the path to the Victory Road opens. Teach one of your Pokemon the Flash, Whirlpool and Surf moves, and then surf southwest from Olivine City or east from Cianwood City to reach the Whirl Islands. Enter the cave on the northeastern island. Show the monk guarding the entrance your Silver Wing, an item you earned earlier in the game when you repaired the radio tower. Continue to the bottom of the cave to face Lugia. Throw your Master Ball at it to capture it instantly, or, if you want a challenge, try to catch Lugia with regular Pokemon balls or dusk balls.
Victory Road
Once you defeat or catch Lugia, head back to New Bark Town and get into the water. Surf east to reach Route 27. Get out of the water when you reach land, and then enter the cave to explore Tohjo Falls. By surfing east on Route 27, you entered the Kanto region, though you cannot explore it fully until you beat the Elite Four. For now, ascend the waterfall to exit Tohjo Falls. Follow the path to reach Victory Road. To get through Victory Road, you need to pass a series of mazes to reach the top level of the cave. Once you do, exit the cave and prepare to face the Elite Four.
Fight the Elite Four
The Elite Four, plus the Pokemon League Champion, use some of the strongest Pokemon types. The first trainer uses psychic-type Pokemon, so take them down with a dark-type Pokemon. Use ground or psychic Pokemon against the second trainer's poison Pokemon. The third trainer uses fighting Pokemon, so fight them with a psychic, flying or ghost Pokemon. To defeat the fourth trainer's dark-type Pokemon, use a fighting Pokemon. Your final challenger, the Pokemon League Champion, uses powerful dragon Pokemon. Defeat his team with an ice Pokemon.