Pokémon Mystery Dungeon: Blue Rescue Team and Red Rescue Team/Silver Trench

Unlocking the Silver Trench
In order to gain access to the Silver Trench you have to go through a series of events. First off you will have to have completed the Pitfall Valley dungeon in the quest that involves Latias and Latios. You must also recruit Zapdos, Moltres, and Articuno. After you've beaten the game the three birds will reappear at their respective mountain's summits. They will be stronger than when you battled them in the main story-line, but you shouldn't have a problem. All three birds share the same friend area in which they will give you upon being recruited. Once both requirements have been met talk to Alakazam in Pokémon Square where he will ask you to investigate a colossal tornado nearby the Legendary Island Friend Area, (which houses Zapdos, Moltres, and Articuno.) There you will receive the Vortex Stone in a cut scene and gain access to the Silver Trench.

The Dungeon
The dungeon starts out easy but you'll be dealing with level 35-40 fully evolved Pokémon by the end. With so many floors to deal with try to use throwing items and basic attacks whenever you can to save up PP. For best results have the leader Pokémon have the Trap-Seer IQ skill. Recruiting wild Pokémon isn't really an option if you plan on recruiting Lugia so just use up their best moves and set them free.

There are lots and lots of monster houses here, so bring the move heat wave or something like that and you'll be leveling up like a chain reaction!

Items
When visiting the dungeon expect to bring more items than you will be picking up. The 99 floors will quickly take a toll on your belly so stock up on Huge Apples for maximum effect, or take a Stamina band and 1 or 2 Huge Apples. The many Sludge and Sticky Traps will require Cleanse Orbs and the many PP-Zero Traps will use up your Max Elixirs. Max Elixirs and seeds stop after 20F, and Grimy Food (the only kind of food in this dungeon), along with Blue Gummis will stop coming after 30F. Throwing items and orbs will appear all 99F so don't worry about using up those.

Boss Battle: Lugia
For all the trouble you went through to get here, Lugia isn't quite as strong as you'd expect. It's level 30 with 800 HP, the hard part, but it's only offensive move is the rather weak flying-type Gust (It also knows Gust and Whirlwind). Remember all of the things you learned about recruiting during this fight, if you screw up you'll have to go through all 99F again. If the leader gives the final attack and the party wasn't too big for the four-star size Lugia upon entering the final floor, it will automatically join your team when defeated.