The easy way to get rid of the reflection is to turn off any lights around the tank and close the curtains-blinders.
Use dark, preferably black long sleeve t-shirt
To get steady images, I use a camera remote control and a tripod.
Turn off the on-camera flash to prevent distracting reflections.
Avoid distortion by placing your camera parallel to the glass wall of the tank.
There are other situations when there isn't an option to close the curtains. In my case, I went to a great, whole window apartment in London, and it was a sunny day too. Not the best option to photograph a massive aquarium. I had a big, black fabric with me, and I set it up in the way where I knew where the reflection would be. I needed to adjust a little bit, and I was ready to take pictures. Easy, right?
Have a look at my client's website if you wonder about having an aquarium at your home at theaquamarinecentre.com.