Spoilers for Bloodborne's expansion 'The Old Hunters' follow.
Ludwig is a tough boss fight. You'll find him after the second lantern in The Hunter's Nightmare, the first area of The Old Hunters DLC.
(Here's how you access the DLC in Bloodborne.)
Step One: Find Valtr
Below the second lantern is a summons spot for Old Hunter Henriett, but she won't help you much in this fight. If you plan on summoning an NPC, you'll want to first join The League, led by the Hunter Valtr.
To join the League, you'll need to hack your way through the Forbidden Forest. Take the lift that leads back around to the lantern (opening the first major shortcut in the area) and you'll find Valtr standing in the hut.
(Note: You can also summon players, but at least during my time in this area there were almost no actual players available to summon, so I stuck with NPCs.)
When you speak with Valtr, you'll be given the option to join his faction. Once you do that, he'll gift you a new Rune: Impurity. Head back to the Hunter's Dream and equip it---if you don't have this Rune equipped some Old Hunters won't show up. Valtr only shows up at the Ludwig fight if you've got Impurity equipped.
Once you've done all that, head back to the second Hunter's Nightmare lantern. Instead of going downstairs to summon Henriett, head out into the pool of blood, sticking to the right to avoid the huge monstrosities waiting to kill you there. Make short work of the enemies near the gate to the right of the tunnel, including the harmless corpse banging at the gate (who will drop five Blood Vials each time) and then head to where the two crows were hiding. Valtr's summon appears there.
Step Two: Fight!
There isn't a perfect method to the Ludwig fight. If you're under-leveled and your gear isn't powerful enough, it's going to be really hard. Ludwig is super aggressive, especially in phase one.
Phase One: Beastly
Ludwig begins the fight on all fours, in beast-form. He'll charge right at you at first, and almost all of his attacks deal huge damage.
Standing in front of Ludwig is suicide. His forward swiping attacks are super powerful, but it's his leaping charge that will easily one-shot you if you're not careful. Stick to his sides and his back, though he'll sometimes stomp and kick at you from behind like a horse.
You can also just stick under his belly, swerving from side to side and avoiding his swiping attacks and charge at all costs. This is dangerous, but not as dangerous as being out in front. I found sticking as close as possible and trying to retaliate as quickly as possible when wounded worked well, as I'd regain life and get in some hits.
You'll also notice that Ludwig is very quick and moves around a lot. He'll dodge out of your way as you come in swinging, and rotate very quickly to face you. Stay on your toes, and keep trying to get in close.
In this form, Ludwig will occasionally leap to the cavern ceiling and then drop down dealing massive damage. Just keep moving and dodging and he'll miss. Ludwig will also spew a magic ooze from his mouth in a long, wide spray. It's very easy to dodge and doesn't deal too much damage. This is another good opportunity to get in close and deal damage.
Phase Two: Holy Moonlight Sword
After about 50% of Ludwig's health is depleted, a cut-scene begins. Ludwig draws out the Holy Moonlight Sword, Bloodborne's iteration on the Souls games' recurring blade.
This phase is a little easier than Phase One, though you'll probably lose any NPC you have with you before long because they're dumb.
Ludwig has a few attacks now, but if you stick close to his legs he's not terribly dangerous. He'll simply swipe at you with his sword which is relatively easy to dodge. Hit him a bunch, and then run away when he lowers the blade for a massive area-of-attack spell.
As soon as that's done, rush back in and go on the offensive. If you stay at a distance, he'll send magical ranged attacks at you that deal a lot of damage and are a bit tricky to dodge.
At this point, watch your life and stamina and just rinse and repeat. It won't be long before you've slaughtered the beast and claimed your Blood Echoes and the Rune Guidance, which you'll need to equip in order to get the Holy Moonlight Sword.
That's pretty much it. Here's a video of me killing Ludwig in NG+ with the help of Valtr:
What great music.
