I am not quite sure, but from the double reflections I think that the normals of the inner parts of the glass are pointing outwards, while the should be pointing inwards. Maybe you should select the inner part of the glass and just flip the normals to see if the double reflections are gone and if the refraction of the glass is working better.
The texture on the ground plane is looking a bit low resolution. Maybe find another one or try creating a procedural one
One last thing: I think it would add to the realism and momentum of the image, if you added smaller glass particles. Not really more glass pieces, but rather just “glass dust”, as a result of the creature breaking the glass. That and some motion blur on the part that are moving fast would make this already very good image great for me!
Other than that: Looking good! The concept is cool, too.