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Basically, it's the single player game mode where you fight all the shadow man and 'bad' versions of the playable characters.
1. Play 450 Brawls
2. Clear Subspace Emissary then Boss Battle Mode with Fox or Falco
3. Clear Subspace Emissary then find him in the Ruins.
Personally I went for the third option when I unlocked him but it's really a personal preference.
If you are unsure how to unlock any other character click the Cheats link above your original post for a nice list provided by our forum members.