Defeating the bear requires poisoning arrows. Lara can do that using mushrooms. You can start collecting them still before you reach the cave that Lara's instinct leads you to. Before you walk out into the open near the camp, climb up the icy wall.
Her instincts lead Lara to a cave with poison mushrooms. To poison your arrow, you need three. Mushrooms grow both near the cave entrance and inside. Head deeper into the cave.
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