Neil,
This is just off the top of my head, and please keep in mind that I'm not exactly an expert an all things Eagle. I don't believe there are many visible differences between the -A and the -C, but the changes, as I remember them, are listed below.
The -C version received a number of improvements over the -A: greater internal fuel capacity, the ability to mount CFTs, several radar, weapons and electronics upgrades, and a higher gross takeoff weight. The landing gear of the -C version was beefed up to handle this, but I don't know how noticeable this would be on a scale model, as I'm unsure as to what parts were strengthened. Also, some time in the mid-1980's, -C versions received the Pratt & Whitney F100-220 engine, which was an improvement over the P&W F100-100 fitted to the -A. Many Eagles fly without the "turkey feathers" on the exhaust cans, so if the Hasegawa kit you are working with has them, you may need to find suitable replacements, from either a second kit or the aftermarket.
I will poke around in my reference file when I can this weekend and see if I can come up with anything more concrete.
HTH.
-YL