Ludwig, the Accursed/Ludwig, the Holy Blade
You've heard of Ludwig from the various Hunters of Yharnam, but you'll come face to face with the accursed man near the Nightmare Church. He's not a pretty sight.
Ludwig is a very tough boss: his horse-like shape means he can gallop around, leap into the air, and still attack you with his claws. The battle will start with a pouncing attack, so be prepared to immediately roll away. You should also keep the battle in the open area - the stairs will trap you and make the camera freak out.
Ludwig's attacks consist mainly of swiping combos, so you should dodge around him, then try to get a in hit during the interim. His charging attack can be avoided by sidestepping, and if he starts stomping all over the place, keep your distance. When he leaps into the air, keep dodging to avoid damage when he eventually lands. But do not attack from the rear, as he'll kick you in defence.
Ludwig's other attack is a white beam that shoots from his second head. This is actually the easiest move to dodge, simply by moving the same direction as the beam. Ludwig is no slouch, but persistence is key.
Oh, and once you get him down to 50% health, he evolves. The second stage of the fight sees Ludwig on his hind legs, brandishing his signature sword. Believe it or not, this stage is slightly easier - his attacks are far more predictable.
His sword combos are telegraphed, and fairly easy to dodge by getting right up against his legs. He also has an area-of-effect blast, so when you see him hold the sword with the point facing the ground, get clear. He may also fire diagonal beams from the sword, and these are easily sidestepped; if he throws a horizontal beam your way, you'll have to time your dodge to pass through it. Finally, he may slam the sword into the ground and unleash energy toward you; keep dodging to the side to avoid the shock wave.
This is a long, gruelling fight, so don’t be ashamed to summon Old Henriette near the Nightmare Church lantern if you need help. Good luck!