This is from the Jamzone - Waltzing 1.
There are only 4 Chords used, each with simple shapes:
The 4 chords are: C add9 - G6 - A7 sus4 - Bb6 (with flat 5th)
Don't worry about the names, as you can see - the shapes are nearly identical. This is done deliberately so you can focus more on your fingerpicking hand.
The fingerpicking pattern is T/3-1-2-T/3-2-1 (the T/3 means pick with both Thumb and 3rd finger together).
Notice this produces an 'oom-pa-pa' feel. That is at the core of most waltzes, the 3/4 signature. Here we double it, so we get 'oom-pa-pa-oom-pa-pa'.
By alternating the notes played by the 3rd finger each time we add a little 'swing' to the music. Simple, but clever stuff!
You will probably find the fingerpicking order a little weird at first, but stick at it. Go as slow as you need to, working just on the first chord. Once you get the hang of it, build up the speed, then work at the next chord. With enough practice you won't even need to think about your fingerpicking, and will find there is more concetration needed for the chord changes! Once you get the hang of it, try it out on other chords you like!
Check out the normal speed audio to get an idea of a good pace to aim for.