From the Super Mario Wiki
Terrifying Invasion is the bonus mission in Treacherous Mansion from Luigi's Mansion: Dark Moon. It is unlocked after Luigi clears the mansion's boss mission, and captures all the Boos from previous missions.
Professor E. Gadd confirms that King Boo is the one who's been sending ghosts to recapture the mansions, and he's sent his strongest soldiers to reclaim the Treacherous Mansion, and if he's successful, he'll take over the whole valley and the rest of the world. Just as in any bonus mission in the game, Luigi has to capture ghosts in the shortest time he can. The order of the rooms and the variety and quantity of ghosts vary each time Luigi plays this mission. The mission is complete when Luigi clears the sixth room.
Interestingly, in this bonus mission, Luigi can access the Bottom of Well again and can leave at anytime using the flower spring that now appears there.
We have an EMERGENCY! The Parascope is detecting whopping paranormal signals in the mansion! Luigi...THE END IS NEAR!
When clearing the Treacherous Mansion of ghosts, what E. Gadd will say to Luigi at the end of the mission differs depending how quickly Luigi completes it:
"Nice work, Luigi. You sure took your sweet time, but you've prevented a major catastrophe. Sit tight -- I'm firing up the Pixelator." (Time over 6 minutes)
"Amazing, Luigi! Simply amazing! You're the finest ghost hunter I've ever laid eyes on! They never knew what hit 'em! Sit tight -- I'm firing up the Pixelator." (Time under 6 minutes)
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