I have two extremely useful tips for Showdowns in Tall Trees. Both involve using your knife.

1. Run full sprint AROUND your enemy, spiraling closer to them as you circle. Run around trees so the trees are between you and your enemy. This will block any lock-ons they try.
2. When you are close enough TACKLE them and SPAM R2. Unless I am out of stamina, I ALWAYS get the kill when I spam R2. This is more reliable than tapping Circle / B and it DOESN'T use as much stamina, if any at all. This works with more than your knife, but use the knife if it's Choose Your Weapon.

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Good luck and have fun. You will almost certainly still be shot because of the chaos :)