Mesh collider on multiple meshed animated character?

I downloaded the free Zombies asset pack off the unity store, and have set up all the animations and everything. When I shoot it nothing happens obviously because there is no collider attached to it.

The problem I face is that there are around 20 different meshes for each part of the zombies body, and no complete mesh for the whole body. I have tried assigning each mesh to a part of the zombies body in the hierarchy but the mesh doesn't follow the movement nor is it in the correct position. This also seems like it would be resource heavy.

What I want to know is how can I get a mesh collider that will follow the animations of this zombie? If I have to compile all these parts and export as a mesh or what have you.. I am really not sure.