Hello @overactivemedia ,
Is your Mesh one Object and do parts of it get left behind?
Then it is probably an issue with the Automatic Weights, that ‘missed’ those parts. You’d need to add Weight to those parts with the appropriate Bone(s), but this is a bit difficult to explain here, especially because I don’t know how much you know already…
I’d highly recommend you taking the time to watch: https://cgcookie.mavenseed.com/courses/learn-how-to-rig-anything-in-blender-fundamentals-of-rigging
