Translation:Žofie does everything more successfully than her uncle.
That's not true, because the definition of better and successful are different. When you are better at something like a sports, it doesn't mean that you are more successful as in award winning. And since they try to teach us the most accurate translation (thank god it would be more confusing otherwise) it's logical that better is not accepted here.
To my native AmE ear, "all" sounds unnatural here. The phrase "...does IT all more successfully..." works fine on the English side, though that may not be a good translation of the Czech original, and I would say that "everything" is probably better here. But if the Czech natives on the team feel that it works, I will add it.