I've determined there is only one near impossible hunt on region 4 armed with the Hammond Valkyrie, and that's the 5 Dromaeosaur hunt, because they simply spawn too close. Every other hunt can be accomplished with the bow more often than not, a lot will have to do with how dinos spawn. On some of the hunts you can easily get oncoming heart shots once you find the spot, and they are one-kill. You can shoot a stegosaurus four times and still get gored if they aren't good shots, one heart shot will drop them. The most fun of all might be the Ingenias hunts where the birds have to be shot twice, and any of the long range ones. I've found you have to really lead your arrow on the distance shots, which is a super nice touch.
So if any of you are bored playing contract hunts waiting on Region 5, put that shotgun down and play with a bow for a while! It will really hone your skills. But when that 5 Dromaeosaur hunt comes, grab an AR, region 2 AR makes you have to make those shots count! Happy hunting.