The dieback could be associated with two things.  The first is winter damage caused by the deep-diving temperatures we experienced during the week of Christmas.  Barberry was affected in our area leading to random stem dieback (= sectional dieback).  Plants can be recovered by pruning out the dead stems.

The second problem would be a fungal infection.  Barberry is susceptible to both Botryosphaeria Canker and Verticillium wilt.  The canker just infects the stems and appears as a sunken area with cracked bark.  Everything above the canker is dead.  The stem is alive below the canker.  If you prune below the canker, you can prune out the infections.

Verticillium wilt is much more serious.  it's known as a "vascular wilt disease" because the fungus plugs the vascular system of an entire stem.  Pruning is not likely to rid the plant of the infection.  There is nothing to spray for either of the diseases.

I'm leaning toward your problem being associated with one of the fungal diseases because I see lichens growing on the exposed branches.  The lichens cause no harm.  They just use the exposed branches as scaffolding and grow best when exposed to sunlight.  While it's not impossible for the lichens to have been there prior to the branch dieback and they started to quickly proliferate, normally, they take a few years to develop meaning the canopy could have been thinning for a while.

You should prune away the dead branches and give the plants some time to see if new growth develops from the base.  Also, make sure the plants don't suffer from dry soils during a drought.  Both of the fungal diseases are strongly associated with plant stress.