Aldrich
Maximum souls: 557,685
Aldrich is vulnerable to fire. Here are some strategies to deal with him, assuming that you first cast Sacred Oath or use the weapon art of the Sunlight Straight Sword before entering the fog wall. In each of these strategies, equip the Magic Stoneplate Ring+2, cast Great Magic Barrier, and consume a Blue Bug Pellet. If you cast Deep Protection, then casting (Great) Magic Barrier would nullify the effect of Deep Protection. In the boss arena, notice the 2 rows of giant pillars. When Aldrich starts to teleport away, stand near a pillar. This should not be a middle pillar, but an end-most pillar, which is a pillar at either end of a row of pillars. Aldrich would re-emerge near the end-most pillar diagonally opposite to where you're standing.
Attune Chaos Bed Vestiges and equip these rings to boost your pyromancy: Witch's Ring, Great Swamp Ring. Throw Vestiges at the boss. Boost your magic defense by casting Great Magic Barrier, equipping the Magic Stoneplate Ring+2, and consuming a Blue Bug Pellet. Refer to the following video for the pyromancy strategy.
Equip a Blessed infused Caestus+10 in the left hand and a Chaos infused Lothric Knight Sword+10 in the right hand. If you want further HP regeneration during the fight, equip the Sun Princess Ring. Spam R1 at the boss. During the second phase, Aldrich would summon a field of fire around him. If you want, equip the Flame Stoneplate Ring+2 to boost your fire damage absorption.
Equip a Sellsword Twinblades+10 in the right hand or a Chaos infused Lothric Knight Sword+10. In the left hand, equip these: Old Wolf Curved Sword, a talisman for casting Vow of Silence, Pyromancy Flame+10. Cast Sacred Oath, Deep Protection, and buff your weapon with Carthus Flame Arc. Enter the fog wall and run to Aldrich, casting Vow of Silence when you're close enough for the spell to also affect the boss. In your left hand, switch to the Old Wolf Curved Sword, 2-hand the Sellsword Twinblades+10, and start spamming L1. When Adrich teleports away, look for where the boss would be, run to the location, cast Vow of Silence, switch to Old Wolf Curved Sword, 2-hand Sellsword Twinblades+10, and continue spamming L1. Note that having 3 items equipped in the left hand might be confusing and/or mess up your focus when switching between the Old Wolf Curved Sword and the talisman for casting Vow of Silence. Before entering the fog wall, buff your weapon with Carthus Flame Arc and un-equip the Pyromancy Flame+10. To boost your damage output, equip these: Lloyd's Sword Ring, Fire Clutch Ring. Vow of Silence nullifies both Aldrich's and your spells. Prior to casting Vow of Silence, ensure you first cast (Great) Magic Barrier and quip the Magic Stoneplate Ring+2.The following video shows the strategy using the Lothric Knight Sword.
Cast Vow of Silence next to Aldrich to negate his spells and yours. Use a fire weapon to hit the boss.