I think I understand why Duolingo gives "Besides pretty, is free." as a possible translation. Portuguese doesn't use the word "it" when someone says for example "It is bad." However, in English we always have a subject. So, it really should be "Besides being pretty, it is free."
This is another case where it's hard to know what answer is being sought because there is no context and I'm not aware of a common analogous expression in English. I can imagine someone responding "Besides, being pretty is free.", just as easily as "Besides being pretty, it's free."
Actually, though you're thinking outside the box (which is good), the portuguese grammar does not allow what you are saying. "Alem de" cannot function as "besides, ...." (standing alone before the comma). In order to do what you are saying, it would have to be "alem disso, ....". "Alem de" requires the following word to be part of the phrase before the comma. Therefore the translation can only be, "Besides being pretty, it is free." Or it can be "Besides being beautiful, it's free." However, I submitted the second example and they did not accept it. This problem needs to be fixed.