Prologue
The first thing you need to do if you are in a hotel is to check in. That is, of course, the case with this hotel too. Go to the front counter and after a short cutscene, you will be shown to your room. You can explore as much as you want, but to progress in the game you have to sleep.
You will be awakened in the night by Princess Peach's scream, investigate the case. Go to the end of the hall and it appears that King Boo is in the wild now. Run away from him and when you reach the end press X to fall down the garbage chute.
Get the Poltergust G-00
You awaken in the Laundry Room. Follow Polterpup to the garage and Polterpup will open a car which turns out to be E. Gadd's. Polterpup will give you a short tutorial with the Poltergust, ZL to blow away, ZR to suck, and ZL+ZR to burst. Your flashlight will Strobulb up when you press A. With that said and done, you can practice by sucking up the mice in the garage. Then, follow Polterpup again.
Gem
White Gem: Use the Poltergust to suck up the cloth on the car that is next to E. Gadd's. Then, Strobulb the switch and it will release the White Gem. This is the only gem you can get on your first visit, expect to get all of them when you have the Dark-Light (2F), Suction Shot (5F) and Gooigi (5F).
Battle your first Ghosts
Use the Strobulb to strobe the switch and run up the stairs to the Grand Lobby. After a short cutscene when going to the main "lobby" itself, battle the ghosts. Get the ghosts in front of you, then strobulb them and suck them up. Other ghosts can be stunned temporarily by slamming them with another ghost, otherwise, they deal 20 HP of damage to the ghosts. Once you have defeated all of them, it's all good, but that's just the introduction!
Gem
You can get 1 gem on your first visit. The rest can be unlocked when you get the Dark Light (2F), Suction Shot (5F) and Gooigi (5F). The purple gem can be got by bursting (ZL+ZR) in front of the counter to get access to a needed key. Strobulb the switch to get the gem.
Go up to the Mezzanine
Go up the stairs to the second floor of the lobby. One door is blocked, so go the other way. You'll find that Professor E. Gadd was also invited to the hotel and captured in a painting. Go through the next door.
Find the Dark Light and Rescue E. Gadd
The room that has the Dark Light is locked and needs a key, so go to the other room. Then, Strobulb the invisible switch (can be seen through the mirror). The safe to the right will spew out the key. Open the door to the storage room and use your Strobulb to open the safe which contains the Dark Light. It can be used to rescue friends from paintings and to reveal hidden objects. Use X to animate the painting of the coins. Then, go back to the Ballroom and rescue E. Gadd.
Mission
A mission requires you to make the invisible objects in the Dressing Room appear (the room where you got the key). This is also one of the features of the Dark Light. The objects to be revealed are a chest (in the southwest corner), a chair (next to the brown table), and a bin (left of the sofa).
Gem
If you're hungry for the gems, the red and green are actually accessible on your first visit. The other gems require the Suction Shot and Gooigi which we will unlock later on. The other gems can be found on the other part of the second floor which is sadly, blocked. For the red gem, in the ballroom, lower the chandelier with your Poltergust, then enter the room to get the gem. For the green gem, suck up all the coats in the left of the Dressing Room. Strobulb the safe to find the gem. You can also get the White Gem from the lobby by shining Dark Light on a missing sofa in the left part, then battle the ghost who has the gem. Then, go to the elevator and continue the story.
B1: How to Defeat Steward
If you go into the Garage where E. Gadd's Car is, you can see that the garage bellhop, Steward is up to no good. It appears that he took on human form to hide is ghostness. When Steward sees Luigi, a boss fight initiates. Time to battle!
Defeat Steward and suck him up
Steward has an HP of 250 and his main attack is to throw the baggage on the floor to hurt Luigi. Run away from where the baggage lands, then flash him with the Strobulb when he's temporarily idle from throwing baggage. It takes about two turns to defeat him, my attempt took three turns. When he's defeated, E. Gadd will show you something.
E. Gadd's Portable Lab
E. Gadd shows Luigi his portable lab where he will reside for the rest of the story. The lab has a map, compatibility for multiplayer, a place where you can talk to E. Gadd,a guide and a gallery. The gallery is where you can see the ghosts you have captured in pods. E. Gadd will give you a few inventions, like the Elevator Tracker and the Virtual Boo.
Install the Elevator Tracker
Go to the elevator to install it. Easy as pie.
Talk to E. Gadd using the Virtual Boo
Use the third option (E. Gadd Hotline) to talk to him. He will send you on a new mission to recover his briefcase from his room on the fifth floor, RIP Suites.
Gem
Use Dark-Light on the painting next to the door of the garage. The gem will pop out.