From the Super Mario Wiki, the Mario encyclopedia
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The Frozen Pit is the final room of the Secret Mine in Luigi's Mansion: Dark Moon. It is where Luigi faces the Shrewd Possessor in the mission Chilly Ride. The room is a deep frozen cavity located underneath the Secret Mine, and has three antechambers, one accessed each time the Possessor's true form is revealed. Because of its depth, the Frozen Pit does not have a visible map and Luigi will experience difficulty when talking to E. Gadd.
The room is accessed after the Shrewd Possessor takes control of the frozen ground in the Workshop and sinks into the ground, causing Luigi to follow it into the Frozen Pit. The icy walls of the inclined trench allow Luigi to ride after the Shrewd Possessor as it descends further into the pit.
Each time Luigi destroys the ice protecting the Possessor, they will both fall into a level chamber adorned with crystals and covered in snow, making it easier for Luigi to capture the ghost. When the Possessor is weakened, it will manifest in another wall of ice and progress further down the Frozen Pit. The final chamber of the Frozen pit has less snow than the other two chambers, making it harder for Luigi to dodge the Shrewd Possessor's dashes.