Like all Pokémon games, Pokemon Mystery Dungeon: Gates to Infinity includes a myriad of Legendary Pokémon. However, unlike the past Mystery Dungeon games, the methods to obtain these specific Pokémon are incredibly varied from the simple encounters in and at the end of Dungeons in the past ones. The methods are as follows

Automatic Recruits

Three of the Legendary Pokémon are automatically recruited throughout the game. First, Virizion joins your team very early on in the game and is Level 20. Keldeo is obtained after you have rescued it from the Glacier Palace and finished the game and is Level 50. Finally, Meloetta will join you when you have opened up the Musical Paradise

No. Pic Name Type
#640 Virizion
#647 Keldeo
#648 Meloetta
Random Missions

Two of the Legendary Pokémon found within the game are only obtainable later on. These Pokémon, Cobalion and Terrakion, are only available through the missions on the noticeboard, with the Legendary in question being the one requesting assistance. These missions will only become available when you have reached the Royal Rank. Once you have completed the mission, Cobalion or Terrakion will join your team. They're at Level 40

No. Pic Name Type
#638 Cobalion
#639 Terrakion
Random Appearances

Three of the Legendary Pokémon are available randomly when you enter various dungeons. Tornadus and Thundurus are found if you get sent to the Golden Chamber - Deepest Part when you enter via specific dungeons. They're found at Level 40. Conversely, Landorus is found completely seperately at random times when in the Breezy Plains dungeon on 8F. It is completely random, and pretty rare, plus it is incredibly powerful as it is Level 70. As these Pokémon will randomly appear, and are not guaranteed to join your after defeating them, then it's best to use the special Gift items; Flying Gift for Tornadus, Electric or Flying Gift for Thundurus and Ground or Flying Gift for Landorus to ensure recruitment

No. Pic Name Type Location
#641 Tornadus
Golden Chamber Deepest Part - Via Quiet Tundra, Dream Island or Moonlight Forest
#642 Thundurus
Golden Chamber Deepest Part - Via Iron Rust Mountain, Large Pit or Smokey Mountain
#645 Landorus
Breezy Plains (8F)
Special Appearances

Finally, on the left-hand noticeboard in the Pokémon Paradise, you will get various special missions to various small dungeons. Occasionally, you will get missions to go to strange dungeons. These areas are just simple battles against various Boss Pokémon. These Pokémon are not recruitable and are incredibly strong and difficult to defeat. One, Ho-Oh, can even be battled as a Shiny Pokémon. These missions can also be played through local multiplayer. The Pokémon are as follows

No. Pic Name Type Location
#249 Lugia
Seasoned Ruins
#250 Ho-Oh
Eternal Ruins
#643 Reshiram
Ivory Peak
#644 Zekrom
Obsidian Edge
#646 Kyurem
Hoarfrost Tower
#646 Kyurem
Turbulent Tor
#646 Kyurem
Turbulent Tor