There are several problems that all make this a difficult retouching problem. Probably the most serious is that the photo has degraded in different ways in different areas. This is a common problem and is usually due to some areas being exposed to light, while other areas are shaded; some areas being in contact with different materials with different chemistry, different water content, different acidity, etc.
Such uneven aging makes a simple global "fix" impossible. To use what you tried as an example, the "curves" that would fix one are would likely be totally inappropriate for a different area of the print.
If there are just two different areas with a fairly sharp, simple boundary between them, one can fix each area separately and then stitch them together. Unfortunately, that's not the situation here. There are many different areas with different amounts of red, purple, yellow, contrast, maximum black density, etc. in each. The only real way to handle this is to treat it as if you were re-coloring a B&W print.
However, since there is some color information present, before I convert the image to B&W, I try to make some quick global adjustments to get the image as good as possible, realizing that the colors at this stage are never going to be very good. Below is the result of global adjustments that I applied in ACR. Compared to looking at the version you posted, it's even easier at this stage to see the different types of degradation in the print. For example, the front of the horse is a different color from his rear.
Once I had a better sense what it might look like in color and got the tonal values fairly good, I then converted it to B&W and did a really quick colorizing job. There have been many previous thread in this forum on good ways to re-color a B&W image - you should look them up. I have absolutely no doubt that other gurus here could do better than I did, but I just wanted to give you a quick idea of what could be done.
Cheers,
Tom M
