Just finished this part, so this I know.
After wasting all my ammo and trying to bareback ride the darn snake, I accidentally discovered that on the two lower walkways that you can "fly" to there is a floor tile that when you step on it takes you down to the main floor, at the same time causing a big spike to momentarily pop out of the floor. So, the idea is to wait until the snake passes over the point on the where the spike comes up and then step on the tile. You hit the snake enough times with the spike and it is history. However, each time you step on the tile you end up back on the main floor, meaning you have to dodge the snake and "fly" back up to the walkway again.