Watch the After You’ve Gone online guitar lesson by Brooks Robertson from Essentials: Boom-Chick Fingerstyle Etudes
As I mentioned before, a great resource to reference when playing an old standard like this is to learn the lyrics. Knowing the lyrics will help you phrase the melody more like a vocalist and usually play more smoothly on the top strings. This arrangement is full of tricky fingerings and movements that can be difficult to execute, so when you get to a spot that gives you any trouble my suggestion is to isolate that part (maybe one measure), and work it out until you can play it consecutively, at least 5-10 times, without any mistakes. Then plug that part back into the given section and keep moving on. Since this tune is full of syncopation, it's especially important to make sure that your thumb (alternating bass) is really keeping a steady groove, no matter how syncopated the melody is. Take note of the specific fingerings being utilized and be sure to reference the tabs and notation when necessary.