First, slice off the arm, the lower part of the "rear" leg, and the end of the tail: the extremities that are not protected by a wall. Then slice off the front leg, starting at the gap at the upper thigh. Clean up any leftover from the lower part of the leg. Now slice off the bottom wall, starting at the rear leg stub and going to the front leg stub. This is a long cut, the angle doesn't provide much leeway, and the balls are almost constantly in the area you want to cut through. Now cut off the head. You can do this in two different pieces, if needed. Now cut off the walls protecting the chest and torso. Another long cut, but not as awkward as the bottom one. Now cut off the butt wall, then the bottom of the tail wall. As quickly as you can, clean up the tail area so that there's no "meat" left next to the wall. It's very common for a ball to get trapped there. You're now down to a single, albeit long and curved, wall. Now it's just a matter of attrition. Cut off pieces away from the wall as much as you can when you can. You'll eventually get there.

This is all from memory, so I might have forgotten something.