"Žofie does everything more successfully than her uncle."
Translation:Žofie všechno dělá úspěšněji než její strýc.
That might be fine, IF the original sentence did not use "more successfully." While the meanings are similar, they are not necessarily identical. It's usually best to use the most direct translation, unless doing so would result in a very strange sentence. But perhaps the native Czech speakers on the team will consider adding your suggestion, if they feel it would be appropriate.