Speak to Sebatian in the "2 Sisiters" next to Galleria Park
Hotel (over the road from the Mersoy). We were told to go there in May.
My mum ordered Sea Bass the night before, he got it in the fish market next day, showed us it on arrival then cooked it there and then. She really enjoyed it, so that might be worth a try. You can always price it first and ask what you are paying for and how much you get for the money.
There were locals eating in there who had also pre ordered fresh fish so that was a good sign for us!