For the sake of precision we must remember that the sea-witch transformed the mermaid. The mermaid desired to be transformed but the mermaid did not transform herself. The mermaid has not only transformed (i.e. changed shape) but she has been transformed (i.e. had her shape changed by something else).
If you are speaking in context and we as your listeners know about the sea-witch's involvement, there is no reason to indicate that in your sentence. Without context, however, you can let us know that the transformation was performed by something other than the mermaid, just use been in your sentence.
The mermaid cannot undo her transformation once she has been turned/transformed into a human
is how I would say it.