I'm not an expert in this by any means as I am just learning Czech myself, but I studied Russian in college, and from what I can hear, 'ň' and other 'soft consonants' are pronounced in Czech very similarly to how they are pronounced in Russian (and possibly other Slavic languages). It's very difficult to describe unless you've had a native speaker explain it to you many times and demonstrate. The best way I can describe it is this: imagine you were about to add the sound 'yee' to the consonant (this goes for ň, d', and t') but stop just short of saying the consonantal 'y' sound. However, forming the consonantal 'y' sound in your palette will create the correct pronunciation of the consonant so that the resonance is closer to your soft palette than your hard.
I would appreciate any corrections and clarifications from native Czech speakers or the Duolingo team.
"Oni žízeň nemají" is accepted. But we have no current report for a translation that uses oni, so we can't tell you why your answer was rejected. Please use the Report button when you believe your answer was improperly rejected, checking first for typos and other small errors. Full Disclosure: The reporting system has gotten buggy lately...