The Celestial Emissary is the boss of the Choir area of the Cathedral (see the "The Choir" trophy for a guide to finding this place). After making your way through the Choir, you will go up a large set of steps and then enter a room with lots of blue bulbs all over the ground – this is where the boss battle takes place.
The Celestial Emissary starts off as a collection of several of the small blue bulb-like enemies that you have seen once or twice before. However, there are a lot of them now, so they're a bit more dangerous than usual. Simply kill a bunch of them, and once you have found the right one, eventually you will see the health bar at the bottom of the screen start to go down. After it goes down a bit, one of the enemies (the Celestial Emissary) will become huge and much more threatening. Fortunately, this boss has so little health that you can take it down very quickly and without much worry – just stay behind it (as always) and attack it with the one-handed version of your weapon. See the following video guide:
Even though the boss room looks like a dead-end, you can continue on from it to earn the "Ebrietas, Daughter of the Cosmos" trophy (see the guide for that trophy for details).