Very good question. Not sure there is one easy solution without changing the basic nature of the game. And that goes beyond the NFL.
I suppose the NFL could do a few things like make the helmets bigger/more cushioned than they are now, get away from playing on artificial turf (carpeted concrete), mandatory rules for healing times for concussions, a max number of concussions (both of which would encourage underreporting). I know the NFL is doling out fines for certain types of hits, but in many cases, it's not a deterrent as some of the hardest hitters make the most money, so the fines only make players at the low end of the pay scale think twice. Suspensions for serious helmet to helmet hits, or fines based on base salary instead of dollars might be a better way to curb the behavior, but unfortunately those hits are the most popular highlight reels.