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Feebas is the last of the three to be mentioned here, and it can only be found on one of six water tiles on the route. It doesn't matter which rod you use, as they all give a 50% of finding this fish each. I recommend just doing one encounter per tile. It's easier and faster than it sounds; I've done it several times.
Evolving Feebas is more of a challenge in my experience. It evolves into the lovely and powerful/bulky Milotic upon maxing out its beauty stat and leveling it up once. You can go to the Berry Master's wife on Route 123 and tell her the phrase "Challenge Contest" to get a Pamtre Berry. Plant it and multiply until you have 5. These can be turned into Pokéblocks (in Lilycove City Contest Hall not far from now) which will put Feebas' "Beauty" stat over 170. Level it up and you'll have yourself an amazing Pokémon. There are other "dry" berry options that can be used to perform this. Kelpsy Berries on the route we found Jigglypuff are good, but you'll need to pair them with some others (Oran and Chest are some examples, but they're lower leveled). Just make sure you don't max out the 255 stat for "sheen" with your Pokéblocks, which is proportional to the feel of the Pokéblocks you create. This means you have a limited amount of blocks you can create, so make sure you use plenty of high leveled dry ones (which typically have a 10% added bonus to them if the Pokémon eating them "likes" the flavor - depends on their nature: Mild, Modest, Quiet, and Rash are all great here).