After you've played for a long time, you should get something called Mermaid Statue. Make a tank and place a mermaid statue in it. It will turn into a mermaid! They prefer not to be alone, though, so put another in.
Don't worry if they get angry when you put the statue in; they will get happy again when the statue turns into another mermaid. There are no mermen, sorry.
Also, make an exhibit. Name it Xanadu. Then look in your animals. You should have a unicorn! Male is black, with red mane. Female is white, with pale yellow mane.