Translation:I do not like fish.
Both さかながきらいです and さかなはきらいです can mean both "I don't like fish" or "I don't like this fish". The が and は don't change it, but the context can change it. Japanese is very contextual and random sentences like that may confuse people.
Like UetzelBrue said, the difference is on the emphasis. It will depend on the context or the question. Let's see:
さかながきらいです is a suitable answer for the questions "What don't you like?", "What food don't you like?" or "What animal don't you like?" because が put the emphasis on what is before it. I mean, that you do not something is already established by the question, so what is really important is the thing you do not like i.e. fish.
さかなはきらいです is a suitable answer for the questions "Do you like fish?" or "Do you like to eat fish?" because は put the emphasis on what is after it. In this case, the information the person wants to know is your feelings about fish i.e. that you do not like it.
Hope it helps :)
Without a context, you should always assume it's something in general, so without the "the". To be specific one should use "kono/sono sakana". If you think about, "I don't like the fish" will not be used in English at all. If you don't like the fish you're eating you'd say "I don't like this fish" (so "kono") and if you don't like the fish the person next to you is eating you'd say "I don't like that fish".
I think (and I'm not 100%) that "I don't like the fish" is meaningless because you don't specify the fisth you are talking about. I mean, "I don't like the fish you brought" makes sense, as well as "I don't like the fish of this restaurant", "I don't like the fish in that aquarium", etc.
I was not given the option to write "hate" here, only "not like"... seems inaccurate.
Random pseudo trivia (is it really the fish though?) :
If this was a Portuguese native saying it it could be a pun with friends or family. さかな (sa ka na) sounds exactly (emphasis on EXACTLY) like "sacana" wich is a word for "rogue like" but on a pejorative level it would be translated in english as "bastard" - but not meaning an illegitimate child, just a someone that is... well, a total bastard xD
"Eu também detesto SACANAs. É compreensível." - "I also hate bastards. It's understandable/relatable."
Source: I'm a "Porch-goose" that loves 初音ミク and already made the bad joke above.