Before leaving the tomb, save the game, preferably in a new slot. Then, if the fight goes badly, just reload and start again. Do not overwrite a previous save made before entering the subterranean lake, since you may need it if you encounter the bug mentioned in the main walkthrough.
Also, try setting the combat mode to Advanced Hold (if it's not already). This makes the part where you have to shoot, holster weapons and quickly throw the grapple (as described below) much easier.
If you start shooting at the bell as soon as the initial cut scene ends, you may be able to distract the serpent before it even notices Lara. (A few players have suggested starting to shoot the bell before the cut scene, but this didn't make a difference for me, playing the PC version.)
As you shoot, you'll see reverberating sound waves start to emanate from the bell (as shown above). When the sound becomes loud enough, the serpent will turn toward the bell, ignoring Lara for a short time.
As noted above, if you set the combat mode to Advanced Hold, as soon as you release the fire button, Lara holsters her guns and you can immediately grapple the lever without having to press an extra button. If you're using standard or advanced toggle mode, press the Target Lock button (G/L1/LT) to holster guns.
As soon as Lara's guns are away, press the Grapple button. Press firmly but only once. Lara should grapple the lever. Then press Interact to pull on the cable, cranking the lever forward and dropping the cage on the serpent's head.
You need to work quickly to grapple and pull the lever before the serpent turns its attention back to Lara, but it's important to work methodically as well. Whichever combat mode you're using, don't tap the holster/grapple/pull buttons repeatedly. It's tempting in the heat of battle, but a firm press on each button with a brief pause between works better. Frantically tapping the grapple key can actually cause the bug mentioned in the main walkthrough.
Once you've succeeded in dropping the second cage onto the serpent's head, run out onto the broken bridge, shooting either of the two bells out in the middle of the pool as you go. The serpent should follow, surfacing near the bell you're shooting. Repeat the same steps: shoot continuously so the bell reverberates. Then, when the snake begins to turn toward it, holster weapons, grapple the lever, then pull to drop the cage.