The sentence given is very basic, it has just mentioned about one person referred to as "she". So, we do not need any comparison with second or third person (positive degree of comparison). If the sentence would have been, "She played the guitar----- than him", then the answer would have been "more skillfully". As in this case there is comparison between two different individuals- comparative degree. On the other hand, "most skillfully" can be used when there are more than two individuals and in that case it becomes a superlative degree. Finally "as skillful as" is a wrong usage for this sentence and it should have been "as skillfully as" which is taken into consideration when the level of talent is the same. For example: She played the guitar as skillfully as her teacher.
So from the above explanation we can understand that the answer should be "skillfully". Option "A" is the correct answer.