There is no such thing as a "certified mermaid" or "certified mermaid instructor", and there is no consensus, much less an "international" one, on what exactly a mermaid is.

Of course there are people who will give you a "certificate" for money, but they made the requirements for this certificate up (and the certificate in itself, of course).

This isn't necessarily a bad thing- if you have no other way to learn to freedive and swim in a tail, and you think it'd be cool to take this course, more power to you.
You could, however, make yourself a certificate with some Editing software, and it would be just as legit.

And let's just say, I really hope it stays this way, because it would suck if some organisation suddenly had the rights to give out the only legit certifications to "be a mermaid", and everyone who wouldn't pay them for it would not be allowed to wear a tail.

(This is, basically, what is going on with Freediving organisations, by the way. No one is allowed to dive in a diving tower without a certification from one of those organisations- no matter if you can freedive or not.
And it costs a fortune. So yea.)