Can I use "descendant" instead of "child" in sentence like this:
As parents achieved something special to get their status, everyone also expects extraordinary things from a descendant.
In principle you could use it in this way. But in practice, we don't normally use descendant (or ancestor) in contexts where both parties in the relationship are still alive. Except perhaps facetiously - but even that wouldn't be common (it might be seen as "in bad taste", given the inherent implication that perhaps the older of two should hurry up and die to resolve the awkwardness of the quirky usage).
[Transcribed from comment]
We wouldn't usually use "descendant" for just one generation difference, or even most likely for two generations. If the issue is that you want to refer to children without implying that they aren't adults, you can use "offspring".
I'm not sure what your sentence is actually asking for, mind you. The corrected version below assumes that you are saying that the children of someone who achieved something special may be expected to do extraordinary things.
"Where parents achieved something special to get their status, everyone also expects extraordinary things from their offspring."