To kill Caragors in Middle Earth: Shadow of Mordor shoot them in the head:

To kill Caragors in Middle Earth: Shadow of War shoot them in the head.

Increase Elf-Shot Arrows
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This is the easiest way of killing Caragors. During combat Caragor’s have attacks that are difficult to deal with so I recommend that you focus on killing them first if they are around. A skill that will help you is the Rain of Arrows skill which replenishes Elf-shot when you perform perfect counters.