Carthus Milkring
The Carthus Milkring raises your Dexterity. It can be equipped with other rings to allow you to two-hand various weapons.
Deacons of the Deep
SL1 Deacons of the Deep, Dark Souls III
This boss is weak against fire and especially weak against lightning. The Raw Dragonslayer's Axe buffed with Gold Pine Resin is recommended against this boss, but you won't obtain the weapon until later in the game. For now, use the Raw Broadsword and save your Gold Pine Resin/Bundle for more difficult bosses because you currently cannot purchase an unlimited amount of Gold Pine Resin/Bundle from the Shrine Handmaid. Charcoal Pine Resin is more than enough for the Deacons. Bring at least Alluring Skull x 10 and use them to distract the deacons.
Defeat the Deacons to receive the Small Doll, an item that allows you access to Irithyll.
Farron Keep
Start from the Farron Keep Perimeter bonfire. Proceed down a path to find the Golden Scroll, located inside a cave. Give this scroll to Orbeck to advance his quest line and you would be able to purchase Hidden Body from him. Hidden Body can help you run past enemies, but you would not be able to cast the miracle without the Scholar Ring because the miracle requires 15 Intelligence. Hidden Body together with the Slumbering Dragoncrest Ring can help you to easily run past enemies to grab any items you need. The Slumbering Dragoncrest Ring is gifted from Orbeck after you have purchased these sorceries from him: Aural Decoy, Farron Flashsword, Pestilent Mist, and Spook. Pestilent Mist is available for purchase after you have given Orbeck at least one sorcery scroll. The Antiquated set is found inside a treasure chest, next to the Golden Scroll. You want the Antiquated Gloves because that armour piece will be used to help you obtain Toxic Mist.
Abyss Watchers
SL1 Abyss Watchers, Dark Souls III
The boss is weak against lightning and vulnerable to backstab. An easy way to deal with this boss is to backstab. Bait out the forward lunge or the spinning jump attack, then backstab.
Defeat the Abyss Watchers, then warp back to Firelink Shrine. Exhaust Hawkwood's dialogue to advance his quest line.
Catacombs of Carthus
Undead Bone Shard at Catacombs of Carthus, Dark Souls III
Grab Large Titanite Shard x 3 in case you need to upgrade a secondary weapon to +6. Find Anri in one of the chambers, exhaust Anri's dialogue, and answer "No". Find Anri again standing near a wooden bridge. Exhaust Anri's dialogue and answer with "No" and "Say nothing". An Undead Bone Shard is hidden inside a Skeleton Boulder. Look for a skeleton that wears a hat, kill that skeleton, and wait for the Skeleton Boulder to smash against some iron bars, thus revealing an Undead Bone Shard.
Location of Carthus Milkring, Dark Souls III
Collect the Carthus Milkring, being careful not to break the various closed jars. This ring increases your Dexterity by three points. Together with the Knight's Ring, you can now two-hand the Claymore as well as two-hand the Zweihander. Two-handing the Claymore would make it easier to clear many strong enemies in the Catacombs and most areas of the game. Consider farming for a Raw Gem to infuse the Claymore. Use the Hollows near the High Wall of Lothric bonfire to farm a Raw Gem. The Carthus Milkring alone allows you to properly two-hand the Composite Bow, which can be purchased from the Shrine Handmaid. Use the Composite Bow together with Poison Arrows to inflict poison on many strong enemies and some bosses. Purchase Poison Arrows from Patches. Note that the Rotten Ghru Dagger infused with a Poison Gem can rapidly poison any enemy that is not immune to poison.
Location of Carthus Bloodring, Dark Souls III
Location of Grave Warden's Ashes, Dark Souls III
SL1 NG+7 Cheese the Fire Demon at the Catacombs, Dark Souls III
Grab the Carthus Bloodring. This ring grants you some extra i-frames, but at the cost of receiving 30% more damage. Receiving more damage should not be among your top concerns. You are likely to be one-shot by most bosses anyway. Pick up the Grave Warden's Ashes. Give it to the Shrine Handmaid and she would sell Kukri, unlimited Titanite Shards, and other consumables. Light the Catacombs of Carthus bonfire. Cross the wooden bridge that leads to Wolnir's arena, break the bridge, and use the broken bridge to climb down. Defeat the nearby Fire Demon, then collect the Black Blade from a Mimic. You can two-hand this weapon while equipping the Knight's Ring, Hunter's Ring, and Carthus Milkring. Light the Abandoned Tomb bonfire.
Smouldering Lake
Undead Bone Shard at Smouldering Lake, Dark Souls III
An Undead Bone Shard is dropped by the Carthus Sand Worm. Use the Ballista to cheese the Worm. The area has Large Titanite Shard x 10 found on corpses. Deactivate the Ballista prior to collecting the treasures. One Titanite Chunk is dropped by a Crystal Lizard located within a cave. These should allow you to upgrade a secondary weapon to +6. Find Horace within the cave where you find Crystal Lizard x 2. Defeat Horace, talk to Anri again near the wooden bridge at the Catacombs, and answer "Say nothing". Doing so should advance Anri's quest line.
Demon Ruins
Undead Bone Shard at Demon Ruins, Dark Souls III
Estus Shard at Demon Ruins, Dark Souls III
Start from the Demon Ruins bonfire. An Undead Bone Shard is found in the area containing Demon Cleric x 2. Near the Old King's Antechamber bonfire is a passageway leading to an Estus Shard. You should now have 12 uses of the Estus Flask and your Estus Flask should now be +7.