It's all based around the simple chord shapes for the song- D,G and A of course. My suggestion is that you download the audio from the record from youtube (it's a much clearer sound than the videos) then play back the solo at a slow speed but the same pitch using Best Practice which is free software, easily findable. If you make sure that your guitar is at exactly the same pitch this should make it much easier for you to figure out what's going on, especially if you combine it with close observation of his fingers on the the video. You can also play back at the same pitch but a lower speed using Windows Media Player by the way, using play/playspeed/slow.
If still struggling maybe ask for help on the Chet Atkins forum http://www.misterguitar.us/forum/search.php?search_id=active_topics- you will need to sign up to the Chetboard- there's some very helpful people on there.
Good luck, don't give up, and I'm sure you'll crack it with perseverence.