Mr3Putt and others have made some good points on explaining, or coming up with an alternative for, a given word or phrase. I've heard it questioned elsewhere, how would one explain colors to a person that has been blind from birth. Blue, Red, White, etc. are all somewhat problematic since you cannot just show the person what you mean by pointing to the blue sky or showing them a red rose or displaying white linen sheets on a bed. To solve this problem different methods are usually suggested using one of the four remaining senses. If it were touch then the methods would include such things as dipping the visually challenged person's hand into a pail of cool water for blue, exposing their hand to something hot for red, allowing them to feel cotton or down feathers for white. In the end, the definition or alternatives are always built from things that are known or can be known. While anyone of these could not be held up as a perfect alternative or exact replica of the original, they are, to me, most effective at conveying something that could not have otherwise been conveyed.
There is however a personal nature to this, and how one would do the same for the masses as a whole is still more problematic. Through some gentle questioning one could perhaps find a place and time in the subject's life where a "Pyrrhic Victory" of sorts happened or was known about and a particular word or phrase that the subject associates that memory with. But, to come up with a word or phrase that does "Pyrrhic Victory" justice for the majority is not easy. It would likely have more to do with the context in which the alternative was used than the alternative itself that would get the general meaning across. Most of the above submissions as alternatives would no doubt do just fine given the correct and sufficient amount of context to go with.
As to why such an alternative would be needed outside the scope of education. There is the matter of writers needing other ways to say the same thing. Alternatives need exist, lest the author find himself/herself using the word or phrase to the point of redundancy and greatly distracting their dear reader or at the very least boring them to tears. Is this not one of the main reasons that the Thesaurus exists?
I, being perhaps the only person who did not know the word or phrase before this thread, am in a unique position to say that the alternatives so far sugested were sufficient to give me the general and fairly accurate idea of what is meant when "Pyrrhic Victory" is used. I found the definitions from the dictionaries by Stella740pl to be quite helpful. I was in need of an alternative that was built from things I already knew.