There are 13 Legendary Fish available to be found, but only 10 of them are accessible before the epilogue. You cannot find any of the fish until you having talked with Jeremy Gill, which does not become available until sometime in Chapter 3 via the 'A Fisher of Fish' mission. Special Lures must be used to catch Legendary Fish. The in-game map can show some of the legendary fish location as unfound even after being caught, Legendary Fish can only be caught once.
Note: There is one bonus Legendary Fish that can be caught, the Legendary Northern Pike, but only once. This fish is caught during the Veteran Stranger Mission set of side missions, which can be skipped, and you do not get to keep the fish, either. There is another fish that Jeremy Gill talks about, the Legendary Channel Catfish, but you cannot catch it.