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The Yao Guai Den
There are two different ways that you can handle this. As you may have noticed, you received some nice mining explosives and a special detonator from Daniel. If you want a slightly easier path, you can just blow up the nest and scare them off. Or you can just go for the direct route, and just charge in and kill them all.
If you want to blow up the nest, then approach the Yao Guai Cave and go inside. The entrance should be clear. In fact, I believe that there should just be three staying far inside the cave in a den. Move forward and then follow the path down toward the flooded section. There should be a small silhouette on the ground marking the spot where you can put the mining explosives. Place one charge here with the interact option.
Move forward through the flooded section. It's not flooded completely, so just swim up for an air pocket if you need one. Keep moving forward until you come out at the path. The path to the left should be clear. Just walk up it and put the explosives on the marker. Backtrack and then go to the right. You can set the explosives on the spot just outside the den. Chances are that you'll anger most of the yao guai inside though.
If you can, try to get the first shot off. A good rifle does wonders. Use some chems if you have to, but just keep firing. If you give Waking Cloud a shishkebab, she can probably handle one of them. That leaves the other two to you. VATS headshots can probably kill one, so I hope you can manage to take out the other with close range shots.
Retreat back out of the cave, and take a few steps back. You can then just push the button on the mining detonator to blow up the cave and seal the entrance.
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Hunting the Yao Guai
If you just want to kill them, then it's fairly straightforward. Don't go into the nest, just follow the road toward Pine Creek Tunnel. You should be able to spot them from a fair distance away, so a good rifle will do wonders. There's room to move around out here, but you'll probably face around six of them. Watch Waking Cloud closely. If she can't survive, then you may need to tell her to just wait.
If you can take them on carefully, draw them out from a distance and use VATS well, then you'll be fine.
Either way, once it's done, you'll get some nice experience and a simple confirmation. No apparent reward for this one.
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All screenshots from Fallout: New Vegas - Honest Hearts DLC