If your run is tall enough and the fence strong enough to support it, put chicken wire or - better yet, but expensive - hardware cloth.
My run fence is supported by metal T-posts, so I use bird netting across the run. It comes in 14 feet wide rolls 25 or 75 feet long. I drape it across the run, zip tying it to the top of the wire fencing and each swatch across the length of the run.
It will certainly keep your chickens in. Once my big rooster was startled whilst on the outside of the run (they free range, now) and he flap-flew up over the fence and onto the bird netting. And bounced three times before his feet got tangled in the netting. I had to cut him out of it. (Then I zip-tied the tear back together.)
So I think bird netting is strong enough to at least deter aerial attacks, if not stop them.
Oh, a 75 foot roll of bird netting is only $19.95 at Lowe's.