Just did two very hard combat shrines one after another. I'd depleted most of my weapons on the first and thought I was almost a goner on the second after a good 10 minutes of chipping away, when it's health almost depleted and it deployed it's devastating laser attack. I just kept hitting away with a weak sword and got hit in the face - but thankfully I was left with a quarter of a heart - I just kept swinging away as it charged up again and managed to destroy it just before it unleashed it's next blast. Got three really nice weapons from that.
Side note, is there a way to avoid those laser targeted attacks in the shrines? Hiding behind a pillar doesn't seem to help.