So, I've looked at Kaylith's SSR Artifacts carefully and I have come to the conclusion that they need improvement.  One of them is about as good as the equivalent SR artifact, and the other one is far worse than the equivalent SR artifact.

Before we get to the SSR artifacts, let's talk about her R artifact: Punishing Wind Rods

These deal 10-20% (Level 1-4) bonus damage on attack.  If you compare this to the effects of other Rare artifacts, it's pretty mediocre.  I think you should adjust these to deal 15-30% bonus damage on attack.  It would still be bad, don't worry, I know you don't intend for it to be powerful.

As far as the SR Artifacts are concerned, they're totally fine.  No buffs needed.   Now, let's talk about the SSR artifacts.

First, we'll talk about how the Great Thunder Nunchaku compares to the Lightning Nunchaku.

At level 1:
Lightning Nunchaku: Increases Attack Power by a stacking 6% per hit for 6 seconds.
Great Thunder Nunchaku: Increases attack power by a stacking 5% per hit for 6 seconds, and attacks deal additional true damage equal to 5% attack power.
Level 4:
Lightning Nunchaku: Increases Attack Power by a stacking 12% per hit for 6 seconds.
Great Thunder Nunchaku: Increases attack power by a stacking 5% per hit for 6 seconds, and attacks deal additional true damage equal to 10% of attack power.

The biggest flaw with the Great Thunder Nunchaku is that it does not increase the gained attack power per hit with each level.  The second flaw with it is that the scale of the true damage bonus is mediocre.

In comparison, the Lightning Nunchaku with a level 4 ability is capable of giving the following benefits, at maximum:
40/m attack rate: +48% attack power (from 4 attacks in 6 seconds)
40/m attack rate with level 1 Hero ability active for +80% attack rate: +84% attack power (from 7 attacks in 6 seconds)
Rune-buffed 60/m attack rate with level 4 hero ability active for +200% attack rate: +216% attack power (from 18 attacks in 6 seconds).

The Great Thunder Nunchaku, on the other hand, has the capacity to give the following benefits:
40/m attack rate: +20% attack power and +10% true damage
40/m attack rate with level 1 ability active: +35% attack power and +10% true damage
60/m attack rate with level 4 ability active: +90% attack power and +10% true damage.

Whether the hero is well-geared and leveled (which it is likely to be by the time it gets the SSR artifact), or just a fresh recruit with a level 1 ability, either way it is sacrificing a lot of attack power to gain only a small amount of true damage.  True damage is good, yes, but it's only about 50-100% more valuable than attack power.  Additionally, as someone with low attack power and high attack speed, Kaylith isn't really the best candidate to effectively utilize a small percentage-based true damage bonus in the first place.

Here's my new suggestion for her artifact's effect:

Great Thunder Nunchaku

Level 1:
Ferocious wind energy whips around Kaylith with every attack she makes, increasing Attack Power by a stacking 5% and movement speed by a stacking 1% for 6 seconds.
Level 2:  7% Attack power and 2% movement speed
Level 3:  9% Attack power and 3% movement speed
Level 4:  11% Attack power and 4% movement speed

The attack power had to scale with level in order for the item to preserve its usefulness, and the movement speed bonus is fitting in all ways: It fits the idea of her having catlike agility, it fits the idea of lightning being fast and deadly, and it serves the purpose of helping her, as a melee damage dealer, to reach her next target more quickly after disposing of her last enemy, allowing her a better chance of getting to attack an additional target while her ability is still active.

Next, let's talk about the Celestial Chainsticks.  On the surface, the idea of an item that increases defense and heals based on attack power looks incredible, but the only problem is that the amount of heal is pretty small, especially considering that she is not a tank hero, and won't benefit as much from healing as a tank would.  She's losing out on her damage role by using this item, so it needs to turn her into a proper tank.  It almost does that; it just needs a bit of a buff.  For comparison, a mere SR artifact for Uldrin grants 5% of his maximum health as healing to all nearby units on every 3rd hit.  Now, 5% of Uldrin's maximum health is a MUCH larger amount than 10% of Kaylith's attack power, in addition to this heal also affecting all nearby units in addition to Uldrin himself.

The Celestial Chainsticks do the following:
Level 1: Vigorous wind energy rushes around Kaylith with every attack she makes, increasing Defense by a stacking 5% for 6 seconds and also healing her for 5% of her Attack Power.
Level 4: Defense increased to 10% and healing increased to 10.00% of her Attack Power

The defense values are fine; it's just the healing that needs improvement.  The amount of healing provided by these items is nowhere near enough to provide a significant amount of healing.  I suggest the following:

Level 1:
Vigorous wind energy rushes around Kaylith with every attack she makes, increasing Defense by a stacking 5% for 6 seconds and also healing her for 12% of her Attack Power.
Level 2: Defense increased to 6% and healing increased to 16% of her Attack Power
Level 3: Defense increased to 8% and healing increased to 20% of her Attack Power
Level 4: Defense increased to 10% and healing increased to 25% of her Attack Power

This amount of healing will still not be great, but it will help some.  Let's bear in mind that her defense and health is considerably lower than that of actual tanks, so she'll still go down fairly quickly in comparison, despite sacrificing the damage bonus of her other artifact; but at least the rate of healing would be enough to feasibly help a bit.