This 1976 Czech movie was brought to my attention recently, and frankly I'm surprised that I didn't already know about it, for shame, hidden gems are fantastic when you find them! According to Adam, who let me know about this movie, it's a co-production between Germany and Czechoslovakia, so there are two different audio versions of this film.
What makes this movie really startling is its use of visuals. It's like someone said: okay, we don't have the technology to make people with fishtails and film underwater, but who's to say that it has to be literal? So they use visual metaphors for the merpeople and underwater world instead, and boy, do they run with it, going for some really unique designs and trippy imagery that make this film really stand out.
Basically, that's a roundabout way of saying that a lot of things in Hans Christian Andersen fairytale are presented in his movie using specific visual cues, and there are no fishtails involved whatsoever.
So how about the story? Considering that I speak neither Czech nor German, I can't comment on how the story was translation for film, but I can say that the atmosphere is gorgeously haunting, with a very melancholy feel thanks to soundtrack and the very dream-like quality to the way the film was shot. From what I can tell it keeps close to the fairytale, and an especially nice touch I thought was how the little mermaid and the dark-haired princess acknowledge each other with kindness and something almost like friendship, the fact that they love the same man doesn't turn into something immediately ugly.
The movie is viewable on youtube: First Part, check it out! And thanks again to Adam for letting me know about this film.