We got our kill tonight by dpsing the right arm whenever it was up. While doing this splash damage also took the left arm down to a low percent. When we killed the right arm and the boss had 12% left, we burned down the left arm for the kill. This may or may not be the best strategy, just throwing the idea out there that ignoring the left arm doesn't have to be a given.
This strategy guarantees that anyone gripped should easily be saved (the arm also removes around three million hp off the boss). Adds are a pain for melee, but it's fairly straight forward.