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One thing you can do is blur the background further. This is achieved by having a lower f-stop (you can think of it as aperture). If you are using a cellphone, this is the same thing as portrait mode on iPhone. 

You could also try to hang the fish with fishing line, so your hands don't show up in the photo, and then using the bandaid tool in photoshop, simply remove the string from the photo. This will give a cool floating fish kinda effect. 

And finally, framing **_always_** matters. In your photo, the background is mostly water, but at the right edge, there is a little green grass. So try to get an even background, so it looks more realistic and cool. 

Lastly, try to make the fish's eyes look towards the camera. Then you can adjust the DOF(Depth of Field) to make the scales look sharp, and the eyes look blurry. I would take a photo, but I'm not allowed to touch fish, so sorry :)