Although it’s possible to defeat the wyvern from down on the ground, it takes forever and is risky. You get stepped on a lot, and trying to hit the head (which takes far more damage than the feet) is maddeningly difficult.
For a better fight, run! Turn left, and dash into the building over there. Don’t fight the Serpent-men inside. You get cooked if you tarry for too long, and the Serpent-men are a pain when you’re distracted.
Sprint past, following the only route around and up through the area. Dodge past a Large Serpent-man at the top, and sprint toward a ladder at the end of the route. This gets you onto a ledge where the Ancient Wyvern’s fire won’t hit. Get onto the stone ledge below there, and fire at the boss from above. You can kill it in total safety, or try a Plunging Attack for a very epic moment. Either way, that ledge turns a long, rough fight into an easy win.
In victory, you’re teleported to the Dragon-Kin Mausoleum, deeper into the region. It’s okay to warp to the previous Bonfire and grab treasure that you missed while running away from the Ancient Wyvern. As a reward, you also receive the Dragon Head Stone.
Three Serpent-men attack in this small room. Draw them back toward the boss’ starting spot to give yourself more room to fight.
As you go up a curving set of stairs, you meet more Serpent-men. Be on the lookout for one that rushes from a side corridor in an attempt to ambush you.
A side area has another Large Serpent-man and additional Serpent-men. It seems like a smart place to bypass as you explore. However, the Serpent-men shoot fire from the upper ledge, harassing you as you cross the next walkway. You’re better off killing them so that the way forward is clear of fire support.
Except for minor loot, the walkway over the boss’ area isn’t useful once the Ancient Wyvern is dead.
Bonfire—Dragon-Kin Mausoleum
The doorway near the ladder leads into the same large chamber that also connects to the Dragon-Kin Mausoleum Bonfire. Therefore, you know where you are, regardless of how you got there. This complex room has two levels. You need to move through it quickly at first because a Serpent-man Summoner on the upper level brings Unkindled into the area to fight you. It won’t stop until you kill the Serpent-man Summoner, so get to the top level as soon as you can. Kill the Unkindled in this room until you gather the Drakeblood Greatsword. This weapon is exotic and nice to have by itself, but it also gets you an armor set later. Travel back to the Consumed King's Garden and look in the Path of the Dragon room for that loot.
A lift takes you down to the starting portion of the area. Once unlocked, this is a shortcut for anyone trying to get inside from the first Bonfire.
Near the bonfire, you can find a small altar. Use the Path of the Dragon gesture next to it and wait for a moment to receive the Calamity Ring.
The outer ledges of the room have some treasure, but watch out for any extra Unkindled that are still there. Also, be wary of a Rock Lizard; these enemies don’t do much damage, but they’re hardy and can push you around. Stay away from the edge of the balcony when you’re fighting one. When you're ready to leave these rooms, walk east. You encounter a hallway and a closed gate (that won't open until you defeat a second boss).
A Dragonslayer Spear is nearby.
After a long hallway of Serpent-men, you face off against one more of their ilk with a Large Serpent-man ally. Back off until you can kill the Serpent-man safely, by any means. The Large Serpent-man is too dangerous of a foe to face with any level of support.
This area has a ladder that leads up to a small tower. Search for treasure up there, and then hop back down.
Another Ancient Wyvern attacks you here. It’s resting on top of a tower, but it comes down as soon as you get into range. This one has less armor, so it’s easier to kill by far. Try to hit the tail as often as possible, which takes much more damage than the feet. If you stand between the feet, you can often hit the tail with most of your attacks.
Dodge when the Ancient Wyvern lifts its feet, and run away if it takes off to breathe.
A Serpent-man Summoner guards this room. It calls Unkindled to the lower floor, where you enter. You can silence this enemy using ranged weaponry from the doorway. Or, you can sprint past the Unkindled that rise, and kill the Serpent-man Summoner quickly with melee attacks. After that, it’s not too bad to defeat one Unkindled instead of an infinite supply of them. Make sure to get Ricard's Rapier from these summoned enemies. If it doesn't drop, use the Bonfire ahead and return here, or let the summoner call additional enemies if it's still alive.
Bonfire—Great Belfry
Rest at the Great Belfry Bonfire. A great bell is nearby, but you’re warned not to ring it if you want to travel the path of the dragon.
The Bonfire leads out to a courtyard with Rock Lizards and Serpent-men. The lowest path goes down to a gate, but this won’t open unless you ring the great bell.
The upper path goes through waves of Serpent-men and Large Serpent-men. There aren’t any new challenges, but the fighting is still intense. East of a broken building you find Dragon Chaser's Ashes. They're on a ledge beside the ruins.
Just after passing that building, you get Havel's Ring+1, but only on New Game +1.
Take a side branch from the courtyard, and climb a ladder. You arrive at a large platform with a dead dragon on top of it. A dangerous Unkindled is there, wielding a heavy club and wonderful armor. Dodge or walk backward to avoid the enemy’s slow attacks, and launch extended combos to punish its poor recovery time. As long as you’re patient, this is an easy fight. You find the Dragon Tooth, Havel's Greatshield, and a Titanite Slab in that yard. Then, you get Great Magic Barrier if you search the ledge west of it.
Follow the path all the way to the top, and use the Path of the Dragon gesture in front of an altar. You receive the Twinkling Dragon Torso Stone.
Major Battle
Return to the Great Belfry and use the bell to darken the skies of Archdragon Peak. Don’t do this until you’ve taken care of all your other looting in the area. The entire region gets very dark when you do this, and a fog gate appears close to the bell. Jump onto the fog that suffuses the area, and walk through the gate when you’re ready for an extremely wonderful boss fight. This is way tougher than the end boss of the game. You do not need to defeat the opponents ahead, and the only reason to do so is because they’re there. And they have treasure. You gain access to this long yard after defeating this special boss encounter. Search the yard fully to get a Thunder Stoneplate Ring (to the west), a Titanite Slab (south), the full Dragonslayer Armor Set (north), and a Covetous Gold Serpent Ring+2 (to the east, but only on New Game +2).