Preface: Don't be turned off by the Umbral Forma. This build is very customizeable and I go over the ways to do that below. The exact build listed is simply my preference.

This build is capable of effortlessly soloing nearly all content in the game. With it you will be completely self-sufficient in regard to energy sustain, and can kill just about anything without help. You are very tanky and have the highest mobility possible in the game, though it does take practice handling an extremely high [Razorwing Blitz] speed bonus. I have over 500 hours played on [Titania] and this, to me, is as good as it gets.

My Exalted Weapons
Dex Pixia
Razorfly Diwata
Non-Razorfly Diwata (current recommendation)

Vasca Builds
Optimal Vasca
Budget Vasca

Alternate Configs
Thermal Sunder Relic Farming

Update 36 changes:
Narrow Minded -> Archon Continuity (1 forma)
Streamline -> Boreal's Hatred (optional)
Primed Heated Charge -> Pistol Pestilence
Accelerated Isotope -> Seeker (optional)
If you don't want to re-forma, the build will still work fine for all the same content it did before.

Quick explanations below, as I do not personally like reading overly long guides. I will assume you generally understand how to play this frame effectively. Plenty of other guides you've probably already read give the basics.

Stuff You Should Use That Isn't Part Of The Build (You'll want to make a loadout)
Because we're always going to want to be in razorwing, that gives us some room to play with the rest of our gear to make it pull some extra weight. A reliable AOE primary can help you out in situations where leaving razorwing temporarily to use it will clear a room faster. We don't have to worry as much about ammo capacity because we only use it rarely. Our secondary can be a kitgun (I use [Rattleguts], any build works) with Pax Bolt. Pop a quick headshot before entering razorwing and keep some extra power strength until you leave it. Equip your sentinel with any [Burst Laser] variant and put both augur mods on it before swapping it out for your Vasca. Set mods will persist regardless! Alternatively, just equip them on your secondary of choice. Augur mods will still work and help you to shield gate. For melee, run a polearm with [Boreal's Contempt] for some extra damage reduction in the air. You can also run all the Gladiator mods on it, but I prefer keeping one with a good build in case I get nullified and need it. [Edun] and [Guandao Prime] are good candidates, or a Zaw with Exodia Brave if you somehow run out of energy. Companions disappear while in razorwing, so a [Vasca Kavat] is my favourite choice, as it will instantly get you up if you get downed, once every two minutes. Djiin looks appealing for this same benefit with potentially infinite uses, but I find it usually dies before it finishes slowly reviving you and fails to do its job. Animal instinct will still work in Razorwing, so make sure to equip it. Using a non-sentinel companion with [Bite] and [Tenacious Bond] will also grant you extra crit damage even in Razorwing. [Reinforced Bond] can also work (though is admittedly much less impactful) if the companion is modded for shields and you reload a few times at the start of a mission. Magus Repair can counteract any chip damage from Arcane Avenger. Madurai will give us more damage, power strength and casting speed, and the best chance at getting Last Gasp kills. Unairu gives us a bit extra EHP and allows us to strip armor and shields on anything that you can't immediately kill with [Dex Pixia]. Zenurik lets you fill up on energy very quickly at the start of a mission without using an energy pad, and can provide a small strength bonus if you double cast the bubble. I find Madurai the most useful overall, but I usually just run Zenurik for lazy convenience and safety on missions with energy pad cooldowns.

[Precision Intensify] VS [Umbral Intensify]
It is true that [Precision Intensify] does increase your DPS by some amount, and I've spent a while comparing them in missions and simulacrum to try and determine what is better. Honestly, the difference is small. Razorwing goes from 354% to 399%, and Nourish from 354% to 299% on my build. I prefer Umbral - even for me that much more speed is excessive, which will impact gameplay more than the little bit of damage. You can change between them anytime with my polarity setup, but if you don't want to spend an Umbral Forma, just go with Precision. Precision will always be better if you prefer a different mod over [Umbral Vitality].

Why [Umbral Vitality]?
Consistency, ultimately. Some bosses will pull you out of razorwing and smack you while you're grounded and don't have [Aviator] and Boreal's mods active. Gas clouds can burn right through your base health even with spellbind's status immunity. What it really comes down to is that our efficiency is already as good as it needs to be, and we are out of strong power strength mods to further increase our damage... but even then, at such a high strength we will only see very dimishing returns from more strength mods. There is no must have mod to put here, so a safety net of some extra tankiness is good QOL. However, if you don't want to spend an umbral forma on [Titania], this is fine to swap out. Other good options (in roughly the order I would use them) include [Vitality], [Primed Vigor], [Catalyzing Shields], [Streamline], [Augur Secrets], [Energy Conversion], [Narrow Minded], and [Quick Thinking].

Endurance missions?
It goes without saying no amount of HP will save you if you're using this build for level cap, but you'll survive a couple hits just fine on standard steel path. Netracells, Conjuction Survival, Deep Archimedia, you'll still be tanky enough to take hits and survive. I consider endurance a niche case, but this build can still adjust to it. For endurance I strongly suggest [Catalyzing Shields] instead of [Umbral Vitality], but you must ensure you are using augur mods on your pistol, as [Brief Respite] will drastically lower your damage output with no ability to proc Arcane Avenger. Note that shield gating with augur mods becomes harder the higher your shield cap is, so [Streamline] should be used over [Boreal's Hatred] once enemies are strong enough to bypass your 80% airborne damage reduction, probably around level 500. (Simulacrum doesn't let me spawn high enough level enemies to test definitively.) In case you're wondering, adding [Boreal's Anguish] doesn't make you invulnerable. Airborne DR is capped at 90%.

(U36) Why are we using toxin now?
Honestly? I don't know exactly why. Something happened with the status update that either nerfed heat or buffed toxin, but it does extremely high damage post-rework in my testing of every element post U36 (even without [Archon Continuity] or even proccing status), and I can't pinpoint exactly why. It could be a bug, an interaction with viral, a byproduct of the enemy armour and resistance changes, or some mysterious fourth thing and I honestly don't know what did it specifically (my expertise starts and ends at Titania specifically, to be honest) but as of now it's the best option and a powerful all-rounder - stripping armour, bypassing shields, and shredding infested. Yes, all exalted weapons apply Archon mods.

(U36) Is blast good yet?
Nope. Enemies sway all over the place in unpredictable directions, throwing off headshots. The aoe damage is pitiful.

Where is [Catalyzing Shields]?
I don't like [Catalyzing Shields] on [Titania] and there is not much more to it than that. If you're wondering why: the AI struggles shooting above them, and with shooting at small targets, and she has a built in dodge chance and an accuracy reducer for enemies, as well as being able to zip around fast to get out of trouble. These are small but they add up - [Titania] is one of the best in the game for personal survivability. Many missions you will not even take damage to begin with. As such, just having augur mods is more than good enough most of the time. If you do like it, consider reversing your hold/tap settings to proc it with spellbind quickly, and replace [Aviator] with [Power Drift]. Again, for long endurance enemies will eventually become very accurate and [Catalyzing Shields] becomes more important. I consider this a niche case so it is not my default reccomendation.

Why [Combat Discipline]?
[Titania]'s passive allows her to constantly heal over time a small amount by casting abilities. Thus [Combat Discipline] does not ultimately damage you much at all, except in extreme scenarios like granum void. We aren't using it for the effect it provides, but instead to keep uptime on Arcane Avenger. This arcane provides a flat critical bonus and has the highest dps increase of any arcane for [Titania], but requires taking damage to proc. Bumping into walls also procs it, but does not deal damage. If you do not have Arcane Avenger, you can run [Brief Respite] for shield gating, [Aerodynamic] for more EHP, or [Corrosive Projection] for more damage. [Pistol Amp] and [Growing Power] are not very impactful, but don't require a forma. [Steel Charge] also allows you to save an extra forma due to it providing more mod capacity than other auras.

[Combat Discipline] is killing me.
I overlooked to mention originally that I run Magus Repair at all times. HP Regen archon shards should mitigate this too - you will only need one or two. Others have mentioned Equilibrium works to keep from dropping too low - you can replace [Umbral Vitality] with this if needed. Adding an extra forma to the build allows you to lower [Combat Discipline]'s rank, reducing the HP lost on kills.

I'm too fast!
Don't sprint unless you know exactly how the tiles ahead are shaped and can navigate your movement quickly enough to accommodate. When traversing, only stack up as many blitz stacks as you're comfortable with, and max out when it's shooting time. Canceling razorwing and re-entering will reset your stacks to help with this. Always keep spellbind up, so you're not doing backflips the whole time. Open doors and hack terminals in operator form to save your blitz stacks from resetting. Hobbled keys only nerf your base flight speed and not the extra speed you get from Razorwing blitz, so you'll only feel it during the times you won't want to. Don't use it.

Why Negative Efficiency?
With Primed/[Archon Flow] and Nourish along with our high duration stat, you have all the efficiency you'll need. Energy orbs will grant over 100 energy. If you run out you can use Zenurik's energy bubble with nourish to regenerate energy at an extremely quick rate, but this will only happen if you go a couple minutes without an energy orb dropping.

Why Nourish?
Nourish provides very high damage, not the highest damage of all subsumes, but its more overlooked and yet more useful feature is the energy multiplier. This applies to all sources of energy, and scales off of strength. Razorwing [Titania] will always want as high of a strength stat as possible, and this allows us to run [Blind Rage] without limiting our time in razorwing at all. Unless your RNG is impossibly terrible, enemies that can drop energy on death will always drop enough energy overall. Our massive maximum energy pool allows us to go long periods without a drop, and also means that getting several energy drops at once will not go to waste. Unlike energize, you can also instantly restore your reserves with a single tick of an energy restore consumable. Nourish can also buff your razorflies - you can use Nourish immediately after entering Razorwing to give them a boost. If you want to run a different subsume, make sure to run Arcane Energize to fufill this role.
Note on Dante Unbound: The nerf to Nourish is fairly insubstantial. In fact, our weapon is skewed further towards slash/toxin procs, which is generally good. I don't notice any difference in sustain, but if you do, use a couple yellow archon shards on energy orb effectiveness, as they stack with Nourish. Other subsumes are still not worth considering as [Blind Rage] becomes unsustainable.

Why Not [Narrow Minded]?
Considering [Razorwing Blitz], we are going to be spamming abilities a lot. [Archon Continuity] is pretty important to our build now that we've switched to toxin, so unfortunately there just isn't space. That said, I don't really notice the difference since Titania spams abilities a lot anyway. Streamline/[Boreal's Hatred] is better for keeping your energy pool up because of how frequently you cast. This also saves a forma. If you think you want more duration, add duration shards, or swap Transient Fortitude for Augur Secrets / [Narrow Minded] for overkill. The value of [Archon Continuity] is in damage output first and foremost.

Why Subsume Lantern?
You can kill anything by looking at it. We do not need CC. We keep Spellbind as a cheap spammable for [Razorwing Blitz], for stagger and status immunity, and we keep Tribute to get more razorflies, lower enemy accuracy, buff our defence, and increase razorfly damage. Each of these buffs is surprisingly useful and is not impacted by our low range. Magus Lockdown is a great CC if you need one, and doesn't take an ability slot.

Why Arcane Pistoleer?
[Dex Pixia] runs out of ammo very quickly. It reloads fast too, but when Pistoleer procs ultimately it is providing more DPS than other arcanes like Arcane Velocity and Arcane Precision, as the bonuses these grant are only additive to other sources. For Velocity especially this makes it not very useful, considering [Razorwing Blitz] will grant more than +300% fire rate already. Precision is strong, though falls off a bit with [Galvanized Shot]. Other arcanes have minimal benefits. Maybe more importantly, pistoleer is fun, and once you get used to the timer it is consistent too. Stopping to get a headshot before going back to spraying everywhere will still save you more time than stopping every second to reload.

Is Archon Intensify worth it?
Archon Intensify can proc off of Titania's passive - however, only on the first tick of healing, and only if that first tick actually manages to restore a health point, so it does not proc at full HP. It cannot refresh until that bonus runs out. While [Combat Discipline] helps to keep the uptime on this mod high, it is still frustratingly inconsistent and requires you to pay constant attention to it by using spellbind before every nourish if you want it to be useful. The Umbral duo of mods is very useful anyway, so I don't bother with all that.

Isn't [Archon Vitality] better? (if using heat)
Yes and no. While you will proc more heat on the average enemy and thus increase the DOT damage, the average enemy tends to die before the second or third tick of damage. This leaves [Archon Vitality]'s advantages in a narrow subset of enemies who are tanky, but also don't have any maximum cap for how many stacks of a given status they can have. Keeping in mind that most bosses have this cap I don't think it's radically stronger and the negatives outweight the positives in most situations.

Archon Shards?
Truthfully, [Titania] doesn't really make great use of shards compared to other frames. But if you want to, just stack whatever combination you prefer of corrosive stacks (One tauforged is sufficient post armor rework), strength, duration, casting speed, energy orb efficiency, HP [Regen], and energy on spawn. I run 2 casting speed, 1 corrosive stack limit, and 2 duration, all tauforged. Don't run secondary crit chance. Strength adds more dps, and also increases the energy you get from orbs on top of that. Consider running 1 or 2 health or shield shards if you're not getting any from mods and not using [Catalyzing Shields].
Update on new shards: Topaz shards with their crit buff may seem appealing, but after finally getting enough of them to run some tests I don't think they're worth it. Like the red shards before them, the bonus is additive, and since we've got Arcane Avenger procced at all times, it still doesn't compare to the myriad benefits of an ability strength shard. [Titania] is also already at her weakest fighting bosses, since she cannot proc Arcane Pistoleer or galvanized mods, and Topaz crit skews that weakness even more. With the Nourish nerf a single energy pad tick no longer puts you at full, so a single shard into spawning energy is worth considering for convenience.