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After retrieving the HM Surf from Solar Cave, a Spinda will wander into Pokémon Square and promptly collapse. You take it to your team base, and it wakes up in front of you and your partner. Spinda explains how he likes to travel, and has been searching for a mirage Pokémon. It gives your partner a Clear Wing, and says that the wing is somehow related to the mirage Pokémon. Spinda heads back to Pokémon Square, and your partner suggests you visit Xatu.
After clearing Great Canyon, Xatu admits he doesn't know much about the mirage Pokémon. However, he does tell you about three Pokémon who are said to be "shadows" of the mirage Pokémon. Xatu tells you about an island to the Northwest called the "Three Fields". One of the shadows lives there, in a field called the Fiery Field. The dungeon is then unlocked.
Inside the Dungeon
Surf is required to enter this dungeon. Once inside, you need to conquer 30 floors to get to the end. Fire Stones can be found on the 29th floor.
On floor thirty, you will find Entei.
Defeat Entei to make it change the Clear Wing into a Red Wing. It will also give you access to the Lightning Field.
You've defeated Entei, and now it's time to continue the quest for the mirage Pokémon. In this dungeon, you again need Surf to enter. There is a chance of finding buried items in the walls, and Thunderstones can be found on the 29th floor.
On floor thirty, you will find Raikou.
After Raikou is defeated, he will upgrade your Red Wing into a Sunset Wing, and give you access to Northwind Field.
You now have two of the three fields cleared. Explore the Northwind Field to find the Pokémon Raikou spoke of, Suicune.
Inside the Dungeon
This is another 30 floor dungeon that requires Surf to enter. On the 20th floor, there is a locked treasure room that contains the Lunar Ribbon, required to evolve Eevee into Umbreon. For non-key holders, Water Stones can be found on the 29th floor, and there is a chance of finding items in the walls on any floor.
On floor 30, you will encounter Suicune.
After defeating Suicune, it will turn the Sunset Wing into the Rainbow Wing. Suicune will tell you that mirage Pokémon can be found at the peak of Mt. Faraway.