Not sure what happened on today's attempt, maybe I wasn't paying much attention, but I got all the way to having to use the random third pet that I had with me. Blackmane, phase 1, never used Dust Cloud and I think that threw me off.
Not sure what issue you could be having. My Direbeak almost solos the entire thing. Gets second pet into immortal round and then Sharptalon just has to pass. Very few crits too if there were any.
One thing I would change about the strat is to not use Predatory Strike if the first phase boss is under 150 HP. Another Swarm will take care of that and then next round of Swarm is on second phase boss, allowing you to Predatory Strike earlier.