The easiest way to finish this quest is to disarm the bear traps, since there are only six on the bridge, and because there are not many enemies guarding them.
If you choose to kill the White Legs sappers, the quest will be somewhat harder because they travel in groups. Two of the White Legs are in a large group to the north, and one is in a smaller group to the south.
Whichever path you choose, you can still go back and disarm the traps or kill the White Legs (whichever you didn't choose) after the quest is completed for extra experience.
The bear traps that need to be disarmed can be hard to spot against the brown coloring of the ground and bridge, especially at night. The Pip-Boy 3000 light helps, but also draws attention to the player from any nearby White Legs.
There can be yao guai and several varieties of gecko in addition to the White Legs around the bridge. After killing enemies on the bridge, it is possible that their corpses may lie on top of a trap, making it impossible to spot without first moving the bodies.
It is possible to complete both optional parts of the quest, but it requires good timing. As you kill the last of the White Legs, you can quickly disarm the final bear trap. However, this will not give you any extra rewards.
It's possible when entering the area that the player will suddenly complete the quest without actually doing anything. This is due to the White Legs either being killed by the various creatures around the bridge, or simply walking into their own traps.