Well, first, if one hand is distracting the other, then we need to methodically eliminate that problem.
With the hammer-on and pull-off parts, the left hand should be able to do this effortlessly like breathing. (easily said).
Playing scales will help your left hand immensely. It is like super food for both hands. Take for instance, the Segovia scales-- or any scales for that matter. Play them every day, loud and clean, with all combinations of right hand-- MA, AI, IM, PI, PM, PA, IMA, MAMI, and make a few more combinations up. Play them vigorously every day. How long is up to you.
After a while the left hand will just breeze through passages and those dreaded hammer-ons and pull-offs. Thus the brain is free to concentrate on the right hand now.