Lara’s idea is to gather poisonous Mushrooms so that she can shoot the bear and kill, or at least disable, it. Climb the handholds at the north side of her current area, and search for Mushrooms as you make your way back to the central part of the region. There is an urn in the next room you reach. Jump up onto a ledge to get that, and then hack your way up an ice wall to proceed (on the west side of the room). Zip line back to ground level afterward, and you’re back in areas that you have already explored.
Hunt around for plenty of Mushrooms. Some are even in a rotting tree back near Base Camp. More are in the northern cave. When you have enough, Lara says to return to Base Camp and make new Arrows. Do this! When you’re in Base Camp, go to the inventory screen and select ammunition and then Poison Arrows.
This is also a good time to learn any new skills. You might also be able to upgrade your Bow if you’ve been scavenging really well. Lara goes to sleep after the crafting is finished. A scene plays, but you wake before morning. Trinity Soldiers are here, and they’re close.
You regain control while Lara is hiding in a bush. Bushes count as concealment.
Multiple Trinity Soldiers are around the area. Two are by your camp. Use stealthy Takedowns to silence them, and don’t forget to search their bodies. There is a Challenge in this area to loot the bodies of three Trinity Soldiers, so you can easily accomplish that right now. The third target is down the hill just a little bit. You can even try a Death From Above attack against him if you wait until he’s wandering under one of the many ledges or hills in the area.
Either avoid the remaining Soldiers on the way to the bear’s cave, or fight them if you’re interested in combat, gaining experience, or grabbing more crafting items from your victims. The cluster of Soldiers underneath the ledge in the east is the most troublesome. They are hard to avoid because you need to pass by them to get to your objective. Attack from long range, while concealed, to kill one or two of them before they know where you are. After that, flee and ambush any pursuers, and then return for the stragglers.
After taking out anyone in your way, return to the bear cave. When you’re there, make sure to stop and get as many Poison Arrows crafted as you can (two for now), and then get the lay of the area outside the cave. That is where the majority of the fight is going to take place.
Sneak into the cave and use a Poison Arrow to slam the bear as hard as you can. It’ll be disabled briefly, so use that time to launch regular Arrow after Arrow into the creature (preferably its head). Save your next Poison Arrow until the bear starts to shake off the first hit. Pound it again and use even more Arrows on it. If you have enough ingredients, you can even craft more Poison Arrows while the bear is stunned, allowing you to attack the beast safely until it dies.
If you run out of Poison Arrows, sprint out of the cave so that you have more room to dodge as the bear starts to charge. Back away and craft more Poison Arrows while avoiding the bear entirely. When you have a couple more Poison Arrows ready, turn to poison and attack the bear again. A crate of Cloth and a dead tree with Mushrooms are both present in the clearing where this battle often takes place. The passage down into the bear’s den also has Mushrooms. If you run out of materials during the fight, see if there are any more nearby. It’s not like you’re going to melee the bear.
Done correctly, your hunt will succeed. The bear soon falls dead. Skin it for a Bear Hide.
Go into the cave and grab a few minor items from the lair. Then, break through the damaged wall at the rear of the cavern. This corridor takes you out of the Siberian Wilderness and into the Glacial Cavern.