Black Swan is a Wind Element Character that follows the Path of Nihility. Her kit revolves around her Arcana mechanic, a debuff status that applies the Wind Shear State and deals Wind DoT upon enemies - also, this debuff cannot be dispelled.
Black Swan is one of the strongest DoT characters and the synergy between her and Kafka makes them well oriented for Dual DoT Team.
Best Cavern Relics
(2) ATK increases by 12%.
(4) For every DoT the target enemy is afflicted with, the wearer will ignore 6% of its DEF when dealing DMG to it. This effect is valid for a max of 3 DoTs.
This set serves its purposes for DoT characters so far as it enhances the Wind Shear DMG by ignoring 6% DEF of the affected enemy.
(2) Increases Wind DMG by 10%.
(4) After the wearer uses their Ultimate, their action is Advanced Forward by 25%.
This set may not increase her DMG well unlike the Prisoner, yet it allows Black Swan to get faster turns and inflict her skill.
Best Planar Ornaments
(2) Increases the wearer's ATK by 12%. When the wearer's ATK is higher than or equal to 2,400/3,600, increases the DoT DMG dealt by 12%/24%.
Having Black Swan with this P.O. set greatly enhances her Arcana's DMG output just by stacking up her ATK for more DoT DMG buffing.
(2) Increases the wearer's ATK by 12%. When the wearer's SPD is equal to or higher than 135/160, the wearer deals 12%/18% more DMG.
Glamoth can enhance her DoT DMG output as long as Black Swan can reach the required SPD for the DMG buff.
(2) Increases the wearer's Effect Hit Rate by 10%. Meanwhile, the wearer's ATK increases by an amount that is equal to 25% of the current Effect Hit Rate, up to a maximum of 25%.
This set only increases the chance for Black Swan to inflict the Arcana Debuff and it doesn't significantly increase her DoT DMG output.
Best Stats

Body
Effect Hit Rate

Boots
SPD

Sphere
ATK% / Wind DMG Boost

Rope
ATK%
Substats
Effect Hit Rate / SPD / ATK% / Effect RES
info
Black Swan only requires 120 % Effect Hit rate to maximize her DMG Buff. Her DoT scales on her ATK and having 135/160 speed for the will allow her to act sooner, this SPD is also valuable for the Glamoth set's DMG Bonus.
Best Light Cones
SourceLight Cone Event Warp
Crystallize
Increases the wearer's Effect Hit Rate by 40~60%. When the wearer deals DMG to an enemy inflicted with Wind Shear, Burn, Shock, or Bleed, each respectively grants 1 stack of Prophet, stacking up to 4 time(s). In a single battle, only 1 stack of Prophet can be granted for each type of DoT. Every stack of Prophet increases wearer's ATK by 5~9% and enables the DoT dealt to ignore 7.2~10.0% of the target's DEF.Reforged Remembrance is Black Swan's Signature Light Cone, it improves her EHR and grants her stacks of Prophet that increases her ATK, and also ignores the target's DEF for DoT.
SourceStellar Warp, Departure Warp, Character Event Warp, Light Cone Event Warp
Self-Confidence
Increases the wearer's Effect Hit Rate by 20~40% and increases DoT by 24~48%.This LC is a great option for increasing her EHR and DoT.
SourceLight Cone Event Warp
Spider Web
Increases DMG dealt by the wearer by 24~40%. After every attack launched by wearer, their SPD increases by 4.8~8.0%, stacking up to 3 times.
If the wearer hits an enemy target that is not afflicted by Erode, there is a 100% base chance to inflict Erode to the target. Enemies afflicted with Erode are also considered to be Shocked and will receive Lightning DoT at the start of each turn equal to 60~100% of the wearer's ATK, lasting for 1 turn(s).This LC is also a good option for Black Swan, it grants the wearer 24% DMG buff and SPD. The erode debuff also help Black Swan's DMG.
SourceLight Cone Event Warp
Wordly Affairs Leave No Mark
Increases the wearer's Effect Hit Rate by 60~100%. After the wearer uses Basic ATK, Skill, or Ultimate to attack an enemy target, there is a 60% base chance to inflict "Unarmored" on the target. While in the Unarmored state, the enemy target receives 10~18% increased DMG, lasting for 2 turn(s). If the target is under a DoT state inflicted by the wearer, there is a 60% base chance to upgrade the "Unarmored" state inflicted by the wearer to the "Cornered" state, which additionally increases the DMG the enemy target receives by 14~22%, lasting for 2 turn(s). During this period, the wearer cannot inflict "Unarmored" on the target.This LC greatly enhances her EHR, it also increases the target's DoT DMG received by inflicting any forms of attack lasting for 2 turns.
SourceStellar Warp, Departure Warp, Character Event Warp, Light Cone Event Warp
Toiler
For every debuff the target enemy has, the DMG dealt by the wearer increases by 12~24%, stacking up to 3 time(s). This effect also applies to DoT.This is a decent universal LC that increases Black Swans overall DMG, but it doesn't enhance her EHR.
SourceEvent, Herta's Store
Quick on the Draw
Increases the wearer's Effect Hit Rate by 20~40%. When the wearer attacks DEF-reduced enemies, regenerates 4~8 Energy.This is an F2P Light cone that increases her EHR and also restores her Energy upon hitting an enemy with reduced DEF - it can be achieved through her skill's DEF debuff.