"Qual a duração do ciclo?"
And you can also say "qual é a duração do ciclo", which means the exact same thing. I guess the verb is somehow implied in this case.
Hey r_i_l_e_y! Yes, you could say that, but it would be an awkward phrase, and it wouldn't be the closest translation (which I assume duolingo is after). The translation of your sentence would be more like "How much time is the duration of the cycle?".
The closest translation of the Portuguese sentence that I can think of is: "What is the duration of the cycle" (instead of "how long...", like duolingo's default translation seems to suggest), and I imagine that that one is accepted. =)
haha I see, it is awkward in English too! Cheers for clearing that up. I had been using "quanto tempo" and "how long" as translations for each other (something I learned long ago) without giving much thought to how literal the translations were.