How do you get the Rank A ending in Luigi's Mansion 3?

Nothing, it's just for bragging rights. The implication is that Luigi restores the hotel to full form if you get the highest rank, as the visual in the background shows the finished hotel restored from the debris after the fight with King Boo.

There's a rank B for those who land between $60,000 and $70,000 at the end of the game and a Rank C below that. It's unknown at the moment if there are ranks lower than C.

As for higher, the original Luigi's Mansion had an elusive Rank S at an enormous sum of money. No one has been proven to have claimed an S-rank yet, but if one exists, it's likely over $100,000. Various people on social media have reported reaching $90,000 and still only receiving Rank A. If a Rank S does exist, it will take the most die-hard treasure hunters to obtain it.

Mostly, you play the game, and loot everything you see. By playing through the game from start to finish while collecting as much as you can while you go, you can usually gather up over $60,000 without trying too hard. But that's not enough.

You'll need to do some extra exploring once you're ready to finish your time in The Last Resort. By far, the best sources of money are Golden Ghosts scattered around the hotel, but finding these friends can be a bit tough, especially if you've already exhausted yourself combing the hotel from top to bottom.

One good thing you can do is simply tour the floors from bottom to top, shining your blacklight everywhere you can and vacuuming up everything you see. You've likely missed quite a few things on your journey up the hotel, or (especially on the early levels) had since gotten powerups to your equipment that you didn't have when you first visited. Just doing a once-over of everything can really help you find more cash.

Avoid spending money on E. Gadd's shop. Though it's not confirmed for certain, it appears to come out of your total when you finish the game.