After you've registered 300 Pokemon in your Browser and completed all 52 quests, you can return to Rand's for the final mission. You may want to stock up on Pyschic types like Gengar, Haunting, Dusklops, etc before this.
Go to Tilt Village and talk to Murph. Take the Union to the Undersea Cavern and swim down. The currents make this a little tougher than before. Some Pinchers attack with a pair of Kingdra.
Once you get to the dark cave, you'll notice there's a new area available in the lower left. Go down there, and you'll have the hardest diving sequence in the entire game. You have to strafe to avoid the yellow laser, but still slip through the gaps in the pink and green fire without staying put too long. It takes practice.
Keep heading right until you get to Blue Eyes, and then begin retracing your steps. When you reach the surface, it's time for one more boss.
Lugia is a tough fight, though you may be ridiculously over-leveled by this point. Charge attacks are actually very helpful because he heals so fast. Quick assists like Togekiss and Stantler are east to do, though psychic attacks are much more effective in terms of stats. You really need to stay on top of him, getting as many loops in as you can to keep him from recovering. You can't depend on assists in this one.
Now you can finally say you've really finished this game.
Taken from... http://guides.ign.com/guides/57609/page_27.html
