Siberian Wilderness - Defeating the Bear

Scramble up the tree and jump onto the ledge to the east of the camp, just like you did the first time you approached the bear cave.

Follow the path toward the cave, picking up some salvage, poison mushrooms, herbs, and possibly hardwood where the path ends at the open area in front of the cave.

There is also a bundle of arrows on the far right side of the open area, a box of cloth to the right of the cave entrance...

...and more mushrooms just inside the tunnel on the left. At this point, make sure you've crafted at least 2 poison arrows and as many regular arrows as possible.

Enter the cave slowly and quietly. Peer around the corner to spot the BEAR enjoying a little snack.

Take aim and shoot it with a poison arrow (RB/Middle Mouse). This will stun the bear but only briefly.

If you aren't wearing the Siberian Ranger outfit and can only carry 2 poison arrows at a time, quickly craft another one now. (Release Aim and hold RB/Middle Mouse/R1 to craft.)

If there's time, hit the bear with a normal arrow or two to do a little more damage.

Then hit it with another poison arrow...

...a few more normal arrows...

...and finally a third poison arrow. The goal is to keep it stunned with poison so it can't charge, while you continue to damage it with normal arrows. On Adventurer or Tomb Raider difficulty, this should finish it off.

If you're using one of the harder difficulty settings, the bear will be tougher. If this strategy doesn't work, and the bear charges, turn around and sprint out of the cave, holding RB/Middle Mouse to craft another poison arrow as you go. Immediately turn around and sprint out of the cave, holding RB/Midle Mouse/R1 to craft another poison arrow as you go.

As you exit the cave, run between the tree and the large boulder on the right.

Then turn around to face the cave opening. Ready your bow and as soon as the bear emerges...

...hit it with another poison arrow to stun it.

Then fire as many regular arrows as you can before the poison wears off.

As soon as the bear starts to move toward you again...

...Shoot another poison arrow, then more regular arrows...

...until it falls down dead. You are then rewarded with XP, plus an Expedition Card Pack the first time you defeat the bear.

Approach the bear's massive carcass and press Interact to harvest bear skin. This rare resource will enable you to craft some cool gear later on.