With a couple of exceptions, there will always be exactly one quest boss present at each quest hub each day, regardless of whether or not there are any dailies at that hub that day. The phase listed after the hub will determine which of the four-to-five bosses is present. However, Bai-Jin the Butcher and the Spirit of Lao-Fe are the exceptions and are always present, but may be the only ones present for their respective hubs that day.
Note that to get credit for the achievement, the adventurer must get first tag on the enemy. If the mob is already most of the way dead and the adventurer helps finish it off, he or she may get quest credit, but will not get achievement credit. Stick around for the respawn and take it from full health to dead.