Check the main walkthrough for an overview of this boss fight and a few general recommendations. The following screenshots show one possible sequence. I won't mention every possible ammo/resource pickup, so keep your eyes open and grab what you can as you go. There are also trees you can climb, bushes and vines to hide in, etc., but this strategy focuses primarily on destroying the statues and fighting Dominguez.
As soon as the cutscene finishes, several Eagle Archers begin roaming the area looking for Lara. You can try to kill a couple of them from the starting position if you like. Or just use Endurance and Focus herbs then run up behind the first statue...
...and press Interact several times....
...to hack at the panel on the back. Disabling the statue frees the Serpent Guard who was entangled in its energy beam.
You can fight them all or just take out a few.
Then turn around and run away from the statue, down toward the right (southwest) corner of the platform.
Near the outer edge, just before the corner, is the mud patch mentioned in the intro. Smear on some camouflage and keep moving around the corner.
If there are enemies close on your heels, turn around and fight.
Otherwise, just keep moving along the west side of the platform, shooting any archers who get in your way.
If you like, you can pause and take cover among the vines to heal and top up your Focus, and Endurance mixtures. Then continue toward the northwest.
Kill a few more archers blocking the way...
...and approach the second statue in the northwest corner.
Use your climbing axe to attack the back of the statue, severing another of the energy tendrils and freeing another Serpent Guard, who then comes after you.
It's your choice, but if he's not right on top of you, you can probably ignore him and head for the third statue, in the northeast corner of the platform. If you turn around and run away from the second statue toward the edge of the platform, then turn right...
...you'll encounter a few more archers on the way. With Focus and Endurance active, you should have time to shoot both...
...before they do too much damage. Continue along the north side of the platform...
...and approach the third statue from behind.
Hack it with your axe to sever the final energy tendril. This frees another Serpent Guard...
...but more importantly, it removes the protective orb around Dominguez so you can fight him.
In a brief cutscene, he powers up and teleports across the platform...
...appearing directly in front of Lara. He swings his obsidian-edged blade and Lara dodges. Here we go!
[City of the Serpent Walkthrough]
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