Depends on the the way the target is moving honestly, you can read and watch a lot of comments from irl people saying that hitting a moving target isn't that easy as it may sound, of course there a million factors at play and automatic weapons make the job easier for pure rate of fire, but even for trained people aren't guaranteed to always nail a shot on a moving person.
Of course it's not impossible, and people are generally running for their lives, in a straight line or something, but here we have a dude who can both move in superhuman ways (quick sways, rolls, sliding kicks can be tricky, for example), but also has a decent experience at dealing with people throwing stuff at him. Of course it's not 1:1 comparison for a bullet and a fireball/energy wave/tornado/kunai etc.. but it's something.
Shooting superhuman dinosaurs in the eyes at first is impressive, but it also depends on how. If you strike the dinosaur while it's still or moving slowly it's one thing, the other is doing some gun-fu type of shenanigan, like Dante or Bayonetta, which is anything but granted. Can the hunter really do a 360 no scope so easily as you claim?
Also, we have to remember Terry will shoot back at him, and the hunter has to deal with that too, even just being throw off balance by having to dodge the wave while Terry may come at him with a jumping attack, a dashing one (which by nature have him moving somewhat faster than when running), might be troublesome, as it doesn't seem like the Hunter can so easily pull of dodging and no-aim-shooting like other videogame characters.
Btw, if you can find more feats, be my guest, I honestly couldn't find anything reliable. For the bullet feat, you may be referring to Billy
blocking a sniper shot directed at Geese, but that occurs in KoF '96.