There are two ways to construct the cat- Dig it out of a mountain and build it from the ground up. The latter should be more difficult and take longer, but obviously, they're both daunting tasks.
That's how I'd do the latter:
If you plan to dig out the cat, defending the fortress/worksite should be very easy compared to the actual work. Generously channel around the cat to make it unreachable by enemies and put a large enough buffer zone between you and your workers.
Assuming you want it to be made entirely out of stone, you should still keep part of the soil layer intact, to enable easy farming. You may also want to restrict most of your contruction to that area, so you won't have to soil your cat with temporary camps.
Start digging out the perimeter. The sides should be the easiest, while the head should be kept at s solid block until later. Same as the tail and the orifice below it. Better safe than sorry. As you progress, build temporary camps on the ever-lowering floor of the dig site.
From this point, you could either dig right down to the feet, or start hollowing out the head first. Personally, I'd dig out the cat in its entirety first, and only then start hollowing it out.
[ January 03, 2008: Message edited by: AlienChickenPie ]