To find the Hylian Loach, you need to fish at the fishing hole during the summer. You know it's summertime in the map, because the inside of the fishing hole's shop is summer-themed.

You need to have a frog lure or a sinking lure. Rent a canoe to fish from, but do not take the shopkeeper along since she will take away your cheat lure. The Hilian Loach is the rarest fish in Hyrule and is a whopping 33 inches.