When most players first enter into this fight, they tend to find that they aren't damaging the boss at all. That's because out of all of the Celestials, only one of them will be the true Celestial Emissary.
None of the attacks he does are that different from any other Celestial and there really is no way to identify him without just happening to hit him on accident. Even when he turns into a giant, it just makes the fight easier because his attacks are a little slower and it is way easier to identify him. The funniest part is that he doesn't even get more damage resistance or extra health, he just takes the same amount of damage from the same attacks.
To succeed, all it really takes is some trial and error when locating the correct Celestial to hit. Once you do find him, all it takes is the same strategy you would use on any other common enemy, attack and dodge when necessary.
Make sure to use a weapon that has a lot of spread, like a two-handed weapon that can swipe, to counter the grouping of enemies. There isn't really a secret to this fight, just hit, hit, dodge, repeat and it'll be over in less than a couple of minutes.