We've done this fight in a variety of ways. Here's what seems to be most successful for us:
First wave of hatchers - let all the hatchlings spawn on one side (kill the other hatcher asap). Soon as the first set of firebombs goes off, kill all the hatchlings.
Second wave of hatchers - let all the hatclings spawn on the other side (both hatchers will run to the same side). Soon as the first set of firebombs goes off, kill all the remaining hatchlings.
Now, the only thing you have to worry about is the boss, and your healers can focus on HEALING YOU. You should also have around 1:45 till enrage at this point, which is plenty of time to get him very close to dead (or probably kill him if your dps folks are very well-geared).
Make absolutely sure you have rage ready to pop shield block every single time the cooldown is up, and use ironshields. I try and set things up so dps is maximized before the enrage phase, while things are less worrysome for the healers. This usually coincides well with me having a shaman and paladin (our OT is always a paladin here, it works great for locking down all the hatchlings at once) in my group for devotion aura, agi totem, stoneskin totem all available for the enrage portion of the fight.
"Frontloading" the fight like this cuts the duration down for us by around 3 minutes, and also allows a very early reset if things go badly during the first 2 waves of hatchers (so you won't be more than about 2 mins into the fight if you need to reset). After all the hatchlings are done, we've been able to win this with only 1 healer alive for the remainder of the fight because the healing difficulty goes down so drastically.
Just my 2 copper!