To complete this quest, the player character must either kill all of the White Legs at Bighorn Bluff, or steal their war totems at Bighorn Bluff. The White Legs are split into two separate camps that are rather close to each other. Each camp has roughly three White Legs, and one war totem is located near the front of the camp. As the totems are relatively separate from the living area tents, choosing the non-violent option should allow an easy time sneaking in to take them so long as they take the White Legs' movement patterns into account.
Once all of the target White Legs are killed, or both of the totems are obtained, the quest is completed, though if the White Legs discover you whilst stealing their totems, the quest will complete, but they will continue to attack. The method of quest completion chosen has no impact on the add-on ending.
According to Waking Cloud, the White Legs consider the loss of a war totem prior to a battle to be a bad omen. She believes that if the totems are stolen, the White Legs in the camps associated with the missing totems will likely refuse to participate in the coming attack.
It is possible to complete both optional parts of the quest, but it requires good timing. If you kill the last of the White Legs, you can quickly pick up the last of the White Legs war totems. However this will not give you any extra rewards.
Sometimes up to two yao guai will appear and attack the White Legs at one of the camps. This makes the quest much easier because usually the yao guai is killed, leaving the surviving White Legs heavily injured.
Same as above, sometimes you may find them under attack by cazadores when you approach one of their camps.
Stealing the war totems has no effect while you're killing the white legs or at the end fight.
xbox360 If you try to take out the White Legs from cover and do not score an instant kill, the specific tribal you injured will immediately become hostile and run to your location, while those not injured will continue to wander the camp passively. [verified]
... or go for the attack
Edit
If you try to take out the White Legs from cover and do not score an instant kill, the specific tribal you injured will immediately become hostile and run to your location, while those not injured will continue to wander the camp passively. [verified]