The fact that the reapers only expose their weak points briefly and cover it immediately if you miss makes them a pain. As someone here pointed out to me, the shotgun is highly effective... They only expose their weak spots at closer range. Shotguns work best at close range. Their spread increases your chance of hitting the Reaper's small hitbox exponentially. An upgraded one does tremendous damage, will stagger it and make it expose additional weak spots.
As long as you keep your cool while it's standing, threatening to impale you and spraying poison, vision-obscuring gasses...