In this video lesson, Albert Lee shows you his approach to chicken pickin'. Chicken pickin' is essentially hybrid picking (picking notes with the pick and the fingers at the same time), but more specific to country music. The notes are often plucked quite forcefully, resulting in a popping sound as the string strikes the guitar.
Albert uses staccato (short, choked notes) here to great effect. A lot of the staccato notes here are played with the picking hand fingers. This is done by quickly muting the strings with the same fingers after you've played them. Pull the strings away from the body slightly to get the 'pop' or 'twang' sound.
The doublestop chords are a mixture of 3rds and 4ths and they outline the basic sound of A, D and E major. Albert moves the same hammer-on lick from bar 2 into the 10th and 12th positions to outline the D and E chords. This should help you get some understanding of where you are in the whole solo. Once you've grasped the basic ideas (such as bar 2) you can start to see how he intertwines chords and chromatic passing notes.