The key to grabbing all your album artwork is one great app: Album Art Grabber
This app is your best bet in executing the desired task as it has one of the highest success rates of any app on the Google Play store of its kind and its very easy to use. After installation of the app, it only takes one click of a button and...Voila! You've got yourself a complete library.
However, as a rule of thumb, some obscure albums may be out of reach for this app. In this case there is the manual option to browse for the work yourself. But the margin of error is so minimal that this manual installation that can occur occasionally is easily overlooked. Best of all...its free!
What are you waiting for? Make your library prettier than ever!