Go on a Ghost Hunt
From the Super Mario Wiki, the Mario encyclopedia
In order to collect this mission's Power Star, the player has to defeat the five Boos on the first floor followed by the Big Boo that appears after the other Boos are defeated. These are the locations of the five Boos:
Once the five Boos are defeated, the Big Boo will appear in the lobby. The Big Boo acts like the other Boos, but it takes three hits to defeat it. Once the Big Boo is defeated, the Power Star will appear on the second floor and a staircase will rise, allowing the player to collect it.
During this mission only, whenever the player character defeats a Boo, the Big Boo delivers the message "Ghosts...don't...die! Heh heh heh! Can you get out of here...ALIVE?" After the last Boo is defeated, it sends a different message: "BOOOOOO-M! Here comes the master of mischief, the tower of terror, the Big Boo! Ka ha ha ha..."
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