This area is short but tricky. It is divided into 3 phases. The next phase will trigger when he runs into the next area.
Phase 1
When you show up in the lair, you will first meet 2 head crabs. Then, you will see a extra-large headcrab with a giant sac hanging from it. Meet Gonarch. As you can probably imagine, the sac is the weakness on this beast. She has 4 major abilities. First she can charge you, Second she can thrash you, third she can spit acid, and most annoying, she can spawn baby headcrabs. For this first section, hit her sac and keep running. You have a lot of space so feel free to use your explosives. After some time, she will knock out some webbing and run through a cave. Before going after her, you will find a floating rock that has a health spring. There is also some ammo near a dead scientist.
Phase 2
Go into the cave and you will trigger a cave in blocking your path to the previous area. Repeat the same thing, but this time, you will find a webbing in the middle of the area. This will allow you to fall into oblivion, or if your lucky you will end up on a spike.
The spikes will give your 3 caves. One will take you to a health spring. The second is an empty cave. The third will give you some supplies and a trampoline that will take you back topside. On the far side of the area, you will find a small hole that will also take you to the empty cave, but safely.
At this point, just keep shooting and dodging until she cuts through the second set of webs.
Phase 3
When she runs through the cave, go after him. You will drop down and continue after her. You will then drop down again into a pit. he will stay on top of the web while you end up underneath. You will also find some much needed supplies. Keep hitting her sac hard and fast. The pit will start filling up with baby headcrabs so do this quickly. Grenades can help keep them down, but don't completely rely on him.
After a short while, she will break the web and join you. Keep hitting her sac and move. She will then collapse. Hit her sac once more from a distance and she will blow up. In her explosion she will open a trap door that you can jump down to. You will then port to the next area.