These fish have a combination of 2 random special attributes (example: exotic diet and musical genius). These are extremely rare try not to spend every day trying to look for them. They cost 40000 shells.
Occurrence
Assuming January 1st of 2016 is day 1 and December 31st is day 366, fish that are extremely rare are available from The Fish Emporium on days that begin with an even number and end in 0, as in 20, 40, 60, and so on. In 2016, this fish appeared on leap day (day 60).