I know it's been a while since anyone has responded to this post, but it takes me a while sometimes. Let me say at the outset that I DO NOT have the answer to your question, but it has puzzled me for months, as well.

I believe that what you're referring to is a fan-tailed something-or-other. I don't know how to get it either, but if I'm not mistaken, there is a website that can help. Do the following:

Go to FORUMS, click on THE GUIDES, then click on FISH TYCOON GUIDE, and finally, click on SPOILERS. When the topic opens, you will find a link to the Clever Arts website. It contains a calculator of sorts that allows you to describe the fish you want to create and tells you the fish you need to breed to make the fish you desire.

Hope this helps...
LadyMaynard

P.S. The only reason that I haven't followed up on this one myself is that I've become engrossed with Virtual Villagers! Haven't had much time for Fish Tycoon since.