I’m practicing this pattern and finding the transition from shape to shape quite tricky. My fingers keep trying to take control and I notice sometimes I end up using a different pair of fingers for the same shape at times. I suppose the answer is practice slowly.
For sure slow practice is the key and for something like this I would try and remain consistent on your fingering choices.
I just had a go at this, and on the first bar I naturally used my second finger for the 4th string, so that finger remains on that string for the whole bar and just slides.
For the second bar, I used my first finger for the 3rd string and that finger stayed on that string for the whole bar, again just sliding up and down the string.
I find that having one finger staying on a string helps for these sorts of patterns.
Here’s a little video, but it’s hard to see my fingering well 
John, they are 6ths with an open string alongside.
Bar 1
Frets 2 & 2 and 5 & 5 … use 2nd finger on D string and 3rd finger on B string.
Frets 3 & 4 … keep 2nd finger on D string and use 1st finger on B string.
Bar 2
Fret 1 & 2 and 4 & 5 … a similar fingering as in bar 1, namely 1st and 2nd fingers.
Frets 2 & 4 … keep 1st finger on G string, stretch 3rd finger out on A string.
I agree with having an anchor finger remaining on one string can help. I found it difficult to get in a groove. I have a tendency to break the pattern.
Thanks Richard.
To me, this sounds like you have to slow it down and commit it to muscle memory, one bar at a time. I guess this advice could be given for around 95% of problems with fingerstyle play 
It is a challenge for me to play slowly. I know I should do it but I let myself get drawn into pushing myself beyond my capabilities.
I think this is a challenge that you’re going to have to meet in order to learn fingerstyle parts like the one you posted.
Try simplifying: play just the bass notes. Then when you can do that (slowly!), add 1 note on the B string per bar and learn how to do that. Then add a 2nd treble note per bar, etc. For me, this is the way to learn these fingerstyle parts.
I too tend to speed up to the point where I’m just on the edge…I find a metronome can really help
John … further
The standard notation above the TAB is, imho, badly written. Given there is a clear A and E harmony, I reckon it should be in the key of either A or E. The person who wrote that score has left their notation in the key of C, therefore they have had to have accidentals (sharps in this case) placed within every bar, rather than the sharps being indicated at the outset.
Notwithstanding that, I have created a TAB only version that shows the fingering underneath. I have also created an audio track with thumb part then 6th part then combined part, all with four repeats, at 45bpm.
Thank you Richard for going above and beyond with your help.
In my original post I think the screenshot of the two bars I posted now appear badly chosen and misleading given your reply. I had wanted to focus my query on the fingers to use for the shapes. To give full context I’ll upload the complete file, which is a practice song a friend of mine has from her guitar teacher.
I’m struggling getting the tempo close to the recording. I’ve made a short clip and would ask if there’s anything I can do with my technique to help with increasing it. I do think I play it a bit better then this clip shows. It’s the usual thing that when I know the camera is on I go to pieces.
If your fingers are going to the right place and your strumming is connecting and all running smooth, increasing tempo is now about playing at a tempo (use a metronome or drum track) and incrementally push the bpm up a notch or two every few days.
If it’s your picking hand that’s holding you back (it looks like it), then you could consider switching from all down picks/strums to alternating down/up. That will present other challenges, but it will enable you to go faster. It will also change the sound somewhat and you will have to decide if you like it that way.
Otherwise, @Richard_close2u 's advice is the way to go: lots of practice with a metronome, slowly increasing the speed.
