Gemstones are very well hidden items in Luigi's Mansion 2. There are five different types for each mansion;
Amethysts are in the Gloomy Manor. Emeralds appear in the Haunted Towers. Rubies are in the Old Clockworks. Sapphires are in the Secret Mine, and diamonds are in the Treacherous Mansion. Each is hidden very well, and the player must have a keen eye to spot clues to where they are. For each mansion there are 13 different gemstones, each with a different shape. Collecting all the gems will unlock a special statue of Luigi for the player to admire. It is decorated with the gems that were collected.
In the Patio, go left and use the Dark-Light Device on the wall, revealing a door to Under the Stairs. Go though the next door to end up on the other side of the fish tank, allowing access to collect the gem.
Reveal some pipes using the Dark-Light on the stairwell of the Tower Lobby, and then reveal a door on the left side of F1 in the Tower Lobby. Use the hitchhiker plant to kill the Carnivorous Plant. Open the chest.
Outside to the left of the entrance is a stove, with a chicken on top. Light the stove and use the flaming chicken to melt the ice around a painting outside. Use the Dark-Light on the painting, and collect the gem.
On the lower left wall is an axe that is hidden with Spirit Balls. Uncover it with the Dark-Light (there is a hidden arrow pointing to it in the ice). Use the Poltergust 5000 on it to find two logs. Put both on the ice to break it, and collect the gem that was inside.
While sliding down be prepared to go to the left. There will be a big spinning wheel blocking a path to a gem. The player must slide through one of the holes in the wheel to get it. This may take a couple of tries.
Go to the very bottom of the mine, in the Crystal Quarry. In that room there should be a portal that can be activated with the Strobulb. Go though and you'll end up in the Chalet. Luigi will land on a chair, knocking the gem from it's hiding spot.
After the Underground Lab, follow the direction the suits of armor point shen checking them. At the last tunnel with no suits of armor, go to the farthest back point and go right. Use the Dark-Light on the painting of a spider web and light it with the fire nearby. Burn the webs you saw along the way for a gem.
Pull on the mammoth trunk in the Ice Age Exhibit to access the Gargoyle Roof. Find three stars around the "room" and shoot them into the giant star made of smaller stars. A gem will fall from the sky upon completion.
Water the spout close to the door, and use the Strobulb on the plant that appears. A gem will pop out. You can find the bucket in the Dark Age Exhibit and the water in the Jungle Exhibit. Use portals to traverse.
Using a Balloon Berry, fly up and right to find a gargoyle with a blue book. Use the Strobulb on it to make it drop the book and fly back down. Put that book into the bookshelf in the Dark Age Exhibit.