Feebas can be found on B1F of Mt. Coronet, which is the room with the large underground lake. However, you can only find Feebas in four random water tiles within said lake, and only by fishing. If you get the correct tile, Feebas will have a 50% chance of appearing. It doesn't matter which rod you use.
It's as bad as it sounds: you need to fish in every water tile until you eventually find Feebas. There are 528 fishable tiles, which means there is a 0.76% chance of any given tile having Feebas. Also, be wary that the Feebas tiles roll over every day, so you should do your entire hunt on the same day. (Also, if you do find a Feebas tile, catch a bunch of them so you don't have to do it again!)
There is one small technique that could help you get Feebas faster, which is mixing records. If you mix records, everybody's Feebas tiles will change to that of Player 1. So you can mix records with friends, then designate sections of the lake to search, and eventually find a "common" Feebas tile much faster than you would've separately.
It's most efficient to trigger an encounter on each tile once, and move on if it doesn't give you Feebas.
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