Translation:My head does not hurt.
This comment is made more humorous by the fact that your avatar (at least the small version on my phone) looks like nico clutching her head in pain
I have seen Duolingo allow "doesn't have a headache" as a legitimate translation for あたまがいたくない(ん)です in a different instance, so it should allow it here as well.
Why is it "atama ga" in "my head hurts" and "atama wa" in "my head does not hurt"?
As usual with the wa/ga differentiation, it's about context. The implication here could be "My HEAD doesn't hurt... But something else does." That's why "wa" translates as "as for". Ga is more for bald statements of fact that don't really depend on context.
In the sentence "Atama ga itai desu" the presumed topic (the known cobtextual topic) is "watashi" and "atama ga" is part of the new information being conveyed in the comment about "watashi." In the sentence "Atama wa itai desu" the known contextual topic is "atama" and "itai desu" is the comment on that topic. This sentence implies a situation in which "atama" contrasts with other conceivable topics. It is "known" in the sense that it is not news that the speaker has one and might say something about it. "Commenting on myself: (my) head hurts" as opposed to "Commenting on (my) head: (it) hurts."
"atama WA ..." means implicitly that you have pain(s) in somewhere else. "atama GA..." is explicit expression only about your head.
When ga is used, the sentence emphasises the subject. On the opposite, wa sentence emphasises the latter part.
It is the "wa--ga" thing again. Japanese has a topic-comment sentence structure. "Wa" generally indicates the topic or focus of the structure and "ga" the subject of the verb in the comment. In "atama ga itai" the topic is actually the speaker ("(watashi wa) atama ga itai.") The Japanese just don't say what can be understood but this sentence is telling you something new about the speaker.
In the sentence "Atama wa itaku nai desu" the topic is "atama" and the comment is about the head as distinct from other possible locations of pain. (When the comment is negative its subject tends to be topicalized. It is still the speaker who is the assumed overarching topic. "(Watashi wa,) atama wa, itaku nai desu.)