Upon arrival, there is a pot with an Emerald in it to the left.
The next section shows your first encounter with the snakes. These snakes can be killed from any side except the front. Approaching them from the front will cause them to strike at which kills you. Continue on the path and kill the snake that has its back turned. Dispatch the other if you want. Before climbing up, to the right on a cliff is a pot containing an Emerald. Continue up and take the path to the right, killing the snake.
Continue forward and you will come into a section with a lot of snakes. Climb up towards the main area with the snakes. Upon climbing, move forward towards where you were facing when you climbed up. Head over to the left, killing the snake. Move forward and kill both snakes to the left and right. Facing the platform that leads to the lever, head right then left to kill the snake guarding the path. Climb up towards the lever and pull it. Doing so moves the gray platform to the left. Before heading down, collect the Twin Snakes piece from the pot above you.
Head back down and eliminate the now vulnerable snake. Quickly go back to the lever and pull it again to open a path to the next area.