Follow the only road and keep going up the set of stairs until you reach the corner where you can hear voices and a short cutscene will play.
Make your way through the bloody water and keep walking until you see the corpse with some arrows. Take the arrows and equip your fire arrows, then shoot the gas to blow it up.
Use the hole to get to the other side and blow up the second gas leak that's blocking your way. There's a campsite in the next area. Use it and you'll get a new entry in Lara's journal. Then grab the arrows and continue deeper into the caverns.
Wait for the unholy ones to get close to the Solarii member, then shoot a fire arrow near the crank to cause an explosion. That should instantly kill all 5 of them.
Head down and find as much arrows as you can. Then pry the gas valve open with your climbing axe and get away from it, then shoot it with a flaming arrow to destroy the makeshift gate.
Climb up the stairs and some Solarii will start walking down the stairs. Hide behind the boxes on the left side and don't open anything.
Wait for them to split up then sneak up on the guy that got left behind and strangle him with F then E.
Now follow the second guy down the stairs and stealth kill him too. Afterwards go back up.
Hide behind some cover then shoot the spot light to draw their attention. The guy in white will get left behind so shoot his head first then shoot the other one.
On the right there's a rock formation that you can climb on. At the top you'll find a gas pipem, pry it open with your climbing axe then shoot the gas with a flaming arrow.
Now climb down and get on top of the metal cage and jump up the wall, then shimmy to the left and get to the next area.
Hide behind the crates and wait for the Salarii to stop talking then shoot the guy that's patrolling below you and the one on the left side near the gas leak.
Jump towards the platform right next to where you're standing and make your way up higher grounds via the climbable walls on the right side.
Follow through the path and you'll arrive at an initiation ceremony for Salarii members. Sneak up the first Salarii and stealth kill him.
Go left then kill the Salarii who's holding a flashlight at the top of the stairs. Don't use your fire arrow or you'll alert the other Salarii.
Now equip your fire arrow and shoot the gas leak right in front of the panel that you're using as a cover. That will instantly kill all the other Salarii in the area.
Then climb up the stairs on the left side and pry open the gas pipe that's at the top of the stairs.
Use your rope arrow to pull on the wooden pillar at the right side of the area, then shoot a flaming arrow at the gas to cause an explosion that'll send the metal cage flying towards the gate on the right side.
Now keep running through the tunnel until you get to the end and climb up the ledge there to find Reyes and the others.
Of course you need to free them first. Take out the Salarii that's patrolling on the right side first.
Then turn to the left side and shoot the guy with a red gas canister on his back and quickly shoot the Salarii on his left before he can call for help.
If he was able to call for help then a fourth one should appear on the right side. After all of the Salarii are dead head to the middle of the room and a cutscene will play.
Grab what you can from the area then head to the left side. There's a gas pipe here, pry it open then shoot it with a flame arrow.
Head up the ramp and make your way to the top of the cage that Reyes and the others are in.
When you get to the top of the cage, draw your bow and shoot a flame arrow at the gas on the left side. It'll send the metal cage flying, once it does shoot the gas right next to it.
Make your way around the cage and back on top. The wall on the opposite side will start to explode.
Jump towards the area that just exploded. You should be able to get there by just jumping towards it through the small opening on the wall.
Pry open both of the gas pipes inside this area. Keep your distance then shoot a flaming arrow at one of them to send the cage flying towards the other side.
After Reyes and the others are safe head for the yellow cages at the end of the platform and use those to get to the other side.
Now just follow the tunnel until you get to the palace.