While the whole character warps to some extent in most cases, the amount of warp can be significantly reduced by judiciously placing fixed points on the character.
Here is a way I did it. I went from the first warping, to the second warping by adding the fixed points shown, using the pen tool on Photoshop
Thanks for that KJerryK. Unfortunayely it didn't work for me... still getting the insane distortion. The arm pushes the chracter away when one drags it towards the charcter and completely distorts when dragging away - see images... I put the fixed points just where you did, but no avail...
Your mesh might be using Rectangle instead of Contour. It's set by default to Auto, which tries to determine the best mode. However, if you have some stray pixels (or "islands"), it will use a Rectangle mesh. Either try switching the layer the mesh is on to Contour explicitly, or seeing if you can remove stray pixels in the artwork. If you'd like us to diagnose the artwork file, feel free to send us a shared link to it. You can send a private message with the link if you prefer. Thanks.