Humane Society

You have to use the buckets of meat to send the packs of unavoidable dogs to sleep. You can also throw the buckets at the human the dogs are following, they will kill him then go to sleep. Make sure you don't waste the buckets though as they do NOT respawn.

The dogs on chains will aggro but can only go to the length of their chain, so just run past them and they will lose aggro. If you stay too close to them (note: being out of melee range does not immediately reset them) and they don't reset, their rage bar will build; when the bar reaches full they will break their chain and will either have to be CCd until the boss is dead, killed, or everyone will have to drop threat somehow. To avoid this make sure you run WELL away from them, so they reset. Alternatively you can throw meat at them too, but it is not necessary and risks you running out of buckets if you miss the big packs.

Also, to state the obvious, do NOT kill any dogs while on the boss encounter itself.

You must not kill ANY hounds in the whole instance up to him.

A more appropriate name for this achievement would have been [No Dogs go to Heaven]