To be honest I don't know what type of fish that is, I'm photographing some inventory for a LFS.
The black background ... Everything I shoot gets processed in Photoshop, some more than others. To alter the background you have to control it, so I make an alpha mask of the fish and save it as a layer. Select the inverse, which in the case will be the background, the I use a gausian blur filter, set to about 150 (which is a LOT of blur), I then adjust contrast and brightness to the still selected background.The black background ... Everything I shoot gets processed in Photoshop, some more than others. To alter the background you have to control it, so I make an alpha mask of the fish and save it as a layer. Select the inverse, which in the case will be the background, the I use a gausian blur filter, set to about 150 (which is a LOT of blur), I then adjust contrast and brightness to the still selected background to get the desired effect, then I reload my fish mask (I want to hide the hard edge that may remain from the blur), modify your selection by making it a 6 pixel border, then I feather this and apply a minor guasian blur to this edge of about a radius of 4.5, don't forget the decimal, just a slight blur. You can HIDE the selection layer to view the results as you may need to adjust the brightness and/or contrast to match your background effect.
After a while these steps can be mastered and near seamless results can be had. The real trick is in not going too far and getting a good initial mask of the fish.