I was thinking about it today, and thought of three ways such an idea could be played out.
Idea one. I would be an olympic swimmer whos kidnapped on your orders and brought to your private island, your own zoo, where kidnapped people from around the world are injected with new DNA to form human/animal hybrids. I would be the latest one, only you would alter me to become a mermaid and keep me, seeing to my training and revelling in the permanent changes to my body.
Idea two. Like the first, only the hybrids rebelled and killed the guards, along with the owner. They died off, but as a mermaid, I could leave and feed properly. I could be found by someone stumbling onto the island, or another island that I've taken as my new home, as the changes to me are permanent.
Idea three. I would be kidnapped and kept by a multi-millionaire as his mermaid. We can talk about how to keep me as a mermaid if this particular one appeals to you, as it wouldnt involve dna or too much surgery.