I'd suggest full Chaos and a Swifty. Glass cannon powers, activate! In all seriousness, I recommend getting a Snarby cap. While shadow defense is debatably negligible there, the damage bonus will help immensely, as well as the increased normal defense, since some enemies there deal a LOT of it, namely Vanaduke and Trojans. The only enemies there that do a significant amount of shadow are slags, which are easy to avoid, and Trojans, which you should try to avoid getting hit by anyway. While Vog is nice and all, ASI isn't the optimal buff for Brandishes, hence why a straight-up damage bonus never hurts. It's what I used before becoming addicted to CTR max on everything. The glacius, blitz, and shiver are all solid and reliable weapons there, but Polaris... Unless you know exactly what you're doing when you're shooting one, people tend to become hostile towards you. The fault lies within the gun itself, not the users. It's just far too easy to abuse, and it won't feel like abusing because of how the gun operates. It's also sometimes used as trolling fodder, hence the monicker, "Trollaris."

I would recommend full chaos with swiftystrike buckler, but as I can see from your loadout (well, you chose Divine veil), perhaps you still are not too confident in dodging shadow damage sources?
Well, we've been saying that Normal defence is very important in FSC every time we see FSC loadout threads, but again, let us say that, more normal defence would be nice...

Also, nice thing you got over there! Fire medium magic hood? Why don't use make it chaos cowl (cancels out the negative resist of chaos) and match with Vog Cub? You will get fine amount of Fire defence and good normal/elemental defence, which are the main damage sources in the Vanaduke boss room, where you cannot solo. Furthermore, you will get Glacius CTR MAX with your UV+Chaos which will help to take out zombies very quickly, and CTR medium on bombs/blitz or alchemers are very valuable. (oh wait have you already made that into Divine Veil...?)

About the bombs, I would recommend you to take Electron Vortex, or Graviton Vortex if you hate playing PvP games to get Krogmo Coins instead of Shiver as you already have a strong freeze from Glacius and Vortex bombs really help to take out monsters quickly over all. And I assume your problem is to solo Vanaduke, so you will be practicing for it more right? But if you're soloing, Shiver+Blitz switching takes a bit too long (the amount of lava will increase too which makes lags) and not very efficient without high CTR/damage on blitz. When you desperately need freeze you could just charge your CTR Max Glacius or through vials. So yeah, I think you should take a Vortex, but don't just listen to me, I'm very biased about Chaos, SSB and Vortexes XD

The guns. There have been many threads about guns in FSC, so you could check them out. But personally, I'd say Argent Peacemaker, Nova Driver. Polaris is also good but I'm not a big fan of it.
The tirnkets should be Sword or Gun damage trinkets in my opinion if you are considering to spend CE/Crowns on the slots. The Shield is very nice, though I'm more on the side of SSB but still I used to run through FSC with BTS and I like it.

CoA not worth it. I never use it in FSC apart from when I'm bombing.

What I think the best from your list is (add Vortex and trinkets though lol)
Sword: Glacius CTR Med
Gun: Blitz, Nova Driver Undead Med
Bomb: Vortex
Shield: BTS
Armour: Vog Cub
Helm: Chaos
Trinket: Sword Med DMG trinket + Gun Med DMG Trinket

That makes
-Glacius CTR MAX, DMG MAX, ASI Med
-Blitz CTR VH, DMG VH
-Nova Driver CTR VH, DMG VH/Max Undead
-Vortex CTR VH

That's why I keep saying to have at least one piece of chaos, for CTR on Vortex and other weapons. All of his weapons are more worthy with high CTR.

Yes, what I meant by "CoA not worth it" is that if he already has BTS and is fine with the shield, there is no point at going defensive all of a sudden. BTS is a nice shield everywhere.

Do you use Chaos in RJP too? I have been doing some research on it, and that is the only situation I would use Chaos for. RJP has almost no status effects. You must be an exceptional player to be able to avoid most status attacks in FSC. Also, I assume that you work to create sets that cancel out the statuses, making your Chaos gear neutral to statuses.
In RJP one could spam their Acheron's charge attack to wipe out slimes in record time.

I use chaos and Skolver in RJP
I use full chaos in FSC I'm better at FSC than RJP for some reason. Lol I used to grind 10+ FSCs per day before joined Unity and when I was in Unity but now I became super lazy as joined EoS and I do FSC weekly lol I'm able todo a run in 13-30 mins depending on the friends to do run with and I do have fire med chaos set which I luckily got before the chaos buff it was cheap but that doesn't matter I'm capable of doing FSC in proto.
Sorry if it sounds like I'm bragging but I don't mean to I just wanted to answer that post. I never say anything about my skills nor how easy this game is or whatever sounds like bragging on forums but I thought it was necessary this time.
Well lets say I'm not that exceptional player I may be exceptional at FSC because of my experience and tendency to make anything efficient, I am fine at PvE but not PvP due to my unique play style not many people use: Arrow Keys.

What I meant by one piece of chaos is that thought it would be hard to use plain chaos set with negative fire resist in FSC for people who are asking for advices on FSC load out and the price of fire UV magic set is high due to the chaos buff so cannot recommend it easily.

Well basic tips...brandish needs dmg bonus high to interrupt properly. CTR is prioritized over ASI for brandishes, but you already have CTR VH which is decent. If you're skilled enough, warmaster rocket hammer is absolutely ridiculous single target dmg and vana solo weapon.

Blitz never interested me personally, but it's likely the easiest way to solo vana.

Since you're sitting on dmg med I'd grab at least one more stage of dmg to help your brandish interrupt decently in combos. If hammer is an option I'd get that too but it takes quite a bit of practice and ASI. Once you know how though, you can essentially one shot trojans.

I never did make a crest of almire...I run in swiftstrike but BTS is perfectly fine. Ideally I think you would switch your divine veil for a kat claw cowl to get more normal, shadow, and dmg/asi.

But really, your current setup would be totally fine with just one 4* dmg trinket.

Have fun xD FSC was never meant to be grinded...I've done it with all sorts of odd weapons and those are usually the fun parties.