Go to career hunt and play challenges. You must beat 30 challenges and 
unlock 8 charter for this gun to be available. It costs 1300$ to buy and 
each ammo cost 7$. It has three shots till you have until you have to 
reload. If you go to optic and buy the best scope for it you are 
virtually invincible. It can even take down a grizzly bear one shot if 
you shot it in the right spot.

1. Try to walk against the wind so the animals will not smell you and it 
isles likely for them to run away. (in the top right of the screen there 
is a small red weathervein, the wind is against you when the small thin 
end is pointing at you.

2. Certain missions will require you to have killed 2 or more animals 
with a knife to unlock it. Equip yourself with a 12 inch knife and hunt 
a predator such as a boar, wolf, or bear, they wont run away from you. 
Don't worry about the animals killing you (I've always been able to kill 
the animal), just keep using the knife.

3. If you are hunting an animal that runs away such as a whitetail deer 
or Dall sheep use a .510 Magnum Bolt-Action rifle, it is the most 
powerful and has the best aim, also buy a 1-10X Adjustable Scope that 
will be attached to your rifle once you buy it to kill animals from 
extreme distances so they don't run away.

4.If you are hunting a powerful animal such as a Brown Bear, Black Bear, 
or Kodiak Bear use a 10 Gauge Gas-Loaded Magnum Shotgun , it is the 
fastest shotgun and most powerful one. If you aim at its head or heart 
area and you should be able to kill h animal with one or two shots.

You can actually use whatever you want to kill these bad boys. I enjoy 
the recurve, but if you aren't experienced use the .510 or whatever else 
ya like. Basically, all you have to do is aim for either the head or 
neck if they are charging, or step around to the side and shoot them in 
the side just above the ribs. The best way to kill them though is to 
shoot them from the side before they see you, and aim for the spot just 
behind their front shoulder. Trust me. If I can kill them with a recurve, 
you can surely nail one with any of the other weapons. And for a really 
fun time, try killing one with the 5" blade. Heheheh.

Go to the level with the grizzly bear and elk deer. 

Go around the big mountain and cross the bridge. Go on the hill with the 
rocks flatend and spot it.

Shoot your gun by it and let it spot you.

Give it a minute and if it does not work move ten yards closer and then 
shoot your gun by it so it can hear it.

When it spots you aim your shotgun dot or point and at it.

When it is running at you put the gun point at the front of the bears 
head about twenty yards out and wait until it gets about 15 yards out 
shoot it in the head.

And you should get a one-shot death on your screen in yellow words.

That's how you kill a grizzly bear.