The update in April 2014 saw the introduction of a new type of fish. Epic fish are each available for one month.
There is a chance to acquire the current monthly fish each time a Mysterious Chest is successfully opened. Epic fish are considered super-rare, as there is no set number of chests to open to acquire each one. Also, any attempts to open chests that do not result in the chest opening will have absolutely no chance to acquire the monthly epic fish.
Once acquired, epic fish are merely for viewing pleasure. They appear on the epic fish list in the collections area of the game, they do not require feeding, nor do they produce pearls or resources of any kind.