Lots of glass windows? Is this a loft apartment with high reflective ceilings, hard uncovered or untreated floors. Very little furniture to dampen reflective sound waves?
Large open dimensional space? Starting with the windows is most likely the real killer in the picture, but also, just a beginning. To properly condition a space like this (assuming I'm correct) is a nightmare for an amateur. Hiring an acoustical specialist would most likely present a cost beyond the value of the system.
Sounds like you'll be chasing this problem around without much true acoustical satisfaction, For a long time.
If your daughter is a "serious listener" as opposed to just a casual listener, the sublime answer may be a good quality pair of headphones. Less hassle and less expense in the long run.
Admittedly however, the drapery treatment, as several have mentioned, plus a lot of cushiony furniture will definitely help the situation, without going crazy. Listening at lower volumes will help as well. But don't rule out component placement. Especially the location and positioning of the primary satellite speakers. I'm certain that some experimentation is this area will yield a number of different results.
I don't know what caliber of equipment she has. If it's just "mid-fi" as I call it, trying to treat the listening space is probably not worth it.
If sound really matters to her, the other consideration might be to move at an opportune time. Then choose you apartment listening space carefully as much as other living space considerations.