It took me some time to figure out who is the Boss - Bloodborne Celestial Emissary :) Boss is the one from those small alien octopuses (mushrooms?), the one who always stays behind. Damage him to 50% and now - run! - he will grow up. His stomps are not that dangerous, however with less than 25% of HP he will use arcane attacks. And stay away from him when he is going to blow up!
Good luck and Have a nice game!

Got 2 runes from him: Communion and Moon Rune which increases amount of blood echos from all kills. Got to Trophies: Celestial Emissary trophy and Rune Master Trophy for getting Moon Rune, I guess.
This boss fight is in the Upper Cathedral Ward - you need a key to open the door into here, search Youtube on how to get this key - a lot of guides have been published already.

Bloodborne Celestial Emissary fight. Bloodborne Celestial Emissary fight tips.

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Watch more of Bloodborne: http://goo.gl/8wAcrP

1st boss: Bloodborne Cleric Fight: https://youtu.be/ubsj6SE5G8o
2nd boss: Father Gascoigne: https://youtu.be/aG654IgWiTs
3rd boss: Blood-starved Beast: https://youtu.be/-3HlvHuOJ6I
4th boss: Vicar Amelia: https://youtu.be/cvyHp6Y7iHE