"who is beautiful"
Raphi, the DuoLingo phrase is perfectly appropriate. The fact that there is no capitalization and punctuation make it clear that the example is not a complete sentence. Duo tests us on individual words as well as sentences, so why not also on phrases that could be part of a sentence?
I disagree. Testing sentence fragments that stand on their own makes sense, especially very early in a course - e.g. for teaching gendered articles in German or the Romance languages it is common to teach just the article and a noun alone (die Frau, das Mädchen; el gato, la gata).
But the whole point of this phrase is that it is dependent on some other part of the sentence - the *, which is beautiful, does ****. Teaching the dependent phrase in the absence of its essential context is confusing rather than clarifying, because there is no meaning associated with it.