As mshelton4 said. Which possessive adjective you use (mi, tu, su, nuestro [and vuestro if you're in Spain]) is determined by WHO is doing the possessing. What form the possessive adjective takes (singular/plural, and gender for the ones that show gender) is determined by WHAT is being possessed.
So to put in front of "deseos" to mean "her desires," we choose su because that is the possessive that can mean "her," and then make it plural, sus, to agree with "deseos." Her desires = sus deseos. ("Sus deseos" can also mean "his desires," "your desires" [formal or plural "you"], or "their desires," but in a normal sentence context should make it clear. (As opposed to an isolated Duolingo sentence.)
If we were saying "their house," we would again choose su because that is the possessive that means "their," and then leave it singular, because "casa" is singular and "su" does not change to reflect gender: "su casa."
I agree that "her" is probably the best translation in this case, since the only possible explicit antecedent for "sus" is "ella." With a larger context, though, the sentence "Ella habló de sus deseos" could definitely mean "...their desires," or "...his desires," or "...your desires," because she could be talking about what someone other than she herself desired.