To hunt? Bears, not because I don't like hunting them but I just don't like the stupid rules the Path of the Hunter challenges give you. "Ooh, kill them with just a pistol!", "Hey, just use your knife, lol!".
To be ambushed by? Boar. They don't do much damage but they charge you without warning, for no reason and at the worst time. The number of times I've been stealthily circling a base planning my route of attack and a boar has charged me from behind, pushing me out into the open and alerting everyone and I end up feeling like Sgt. Powell from Die Hard. Welcome to the party? Yeah, thanks. Thanks for that.
I hate Jaguars. I always die because I have a bow or smg when they attack, and I can't reload or use a syringe. I end up knifing the hell out of them too. Wouldn't be a problem with a shotgun, but I never have one equipped when I'm ambushed, or can't switch fast enough.
I also hate cassowaries(sp?) They don't attack much but they're annoying, so I love killing them.
The animals in this game are no where near as annoying as the predators in Red Dead Redemption.
Hordes of ninja bears....random cougar attacks...so damned annoying.
I used to hate tigers, but late in the game once you get all those super high-damage weapons, most animals aren't much of a problem. Deer hunting was always super annoying though. So hard to find, and you can only kill one and then the rest disappear.