All you have to do is catch an Epic (purple coloured) Fish. There are several types of rare, epic fish in the game but as long as you are going for the 'Angler' and 'Fish Watcher' Achievements you'll get one along the way. I caught mine in the first dungeon so don't panic if you fish a hole dry, you can always come back again later or fish another hole as you progress through the game getting better equipment to catch better fish.