[Wukong] is one of the most versatile frames, being a relatively tanky frame that is still quite capable of dishing out some serious AOE damage. This build, however, will be focused primarily on trying to use a whole slew of synergies as a little experiment just to see how much damage we can reasonably obtain against without completely sacrificing survivability (I do want this to be useable, ya know :) ). Sometime pretty soon, I will also be making a build to see how much raw damage we can obtain in a single hit (due to the finicky nature of my planned approach, this would be more of a theoretical calculation assuming a perfect, Simulacrum-style environment), in addition to a possible anti-Sentient build.

The Abilities

In order to gain a better sense of which direction we need to go to maximize our melee damage, we need to first examine [Wukong]'s abilities, and how exactly they will help us.

1. Celestial Twin

This ability spawns a Celestial Twin, which has a health, shield, and damage boost. It just so happens that this ability is also the one that will help us the most in achieving a massive amount of single-target damage output. Why? This ability essentially allows you to use both your primary and melee weapons at the same time. Here is a bit more detail on how this ability will help us deal as much damage as possible:

1. When you have a ranged weapon (i.e. primary or secondary) equipped, [Wukong]'s twin will equip the melee, and vice versa. The weapon equipped by the twin also has a fixed 2x damage multiplier; however, since the twin generally has a very low attack speed when equipping melee weapons, we will find that it is not necessarily better to have him use the melee weapon.
2. [Wukong]'s twin still has to reload, but doing so does not consume your ammo reserves. This means that the twin effectively has a 100% ammo efficiency.
3. When using a primary or secondary weapon, the twin will actually aim (this will be important later).
4. The twin normally attacks random targets, but activating the ability again while aiming at a valid target (pretty much everything except capture targets) places a marker above the target, forcing the twin to attack said target. Once the target dies, the twin will start attacking random enemies again until you select a new target.

It should be the first ability you use, and you must prioritize keeping the twin alive.

2. Cloudwalker

This ability is your self-healing/cleansing ability, speeds you up, and makes you immune to gravity and inertia (i.e. UFO style flying). It prevents you from attacking, but makes you and your twin completely immune to damage, prevents/removes all elemental effects (including those caused by the pesky Grineer door traps), and temporarily stuns enemies within a certain range of you; however, non-elemental effects (including movement speed debuffs and energy leech effects) are not prevented or cleansed. Additionally, it heals you and your twin by a certain amount of your respective max health pools for each meter traveled. One important thing to note is that, although the twin benefits from all the effects of this ability, it does not actually enter the cloudwalker state, and can still deal damage for the duration of the ability.

3. Defy

This ability makes both you and your twin immune to damage for a short duration. Additionally, any incoming damage is stored, and then released to all enemies within range with a certain multiplier that scales with ability strength. When the duration expires, the ability cleanses all elemental effects. Finally, depending on the amount of absorbed damage, you will gain up to 1500 additional armor (this cap does NOT scale with ability strength). With [Wukong Prime]'s base armor of 275, this amounts to a total damage reduction (DR) of about 85.5%.

4. Primal [Fury]

Both you and your twin draw [Wukong]'s [Iron Staff]. Much like [Mesa]'s pistols, Valky'rs claws, and [Excalibur]'s sword, the staff's base damage scales with ability strength, and it can be modified as a separate weapon. While this might seem useful, it prevents you from using two separate weapons simultaneously, which is what this entire build is based on. Therefore, we will be mostly disregarding this ability.

The Strategy

OK, with all that out of the way, here's the game plan:

The Weapons

Before we consider how to build our [Wukong], we need to consider what weapons we want to use.

Primary

We will primarily (get it?) use the primary weapon as an applicator for the three primary status types we are looking for: Corrosive, Heat, and Viral (this damage type is REALLY important, since it provides a maximum damage multiplier of 4.25x, or a boost of 325%!!!). However, since Corrosive and Viral both share the Toxin component damage type, most weapons are not actually able to apply all three. One weapon, however, stands out as a very good choice in this situation: the [Phage] shotgun. With a high native multishot of 7, rate of fire of 12 rounds per second, and a high status chance of 15.5% per projectile, this weapon is perfect in pretty much every way. Even its high ammo consumption is not a concern, since we will be using it on the 100% ammo-efficient Celestial Twin, anyways!!!

Here is the Phage build I would use. It's designed to proc as many status effects as possible within the shortest amount of time possible. However, [Phage] does have a 0.6s period during firing, where it focuses its beams to a single point while aiming.

Secondary

You could bring a secondary weapon that serves the same purpose as the primary, if you want, but there is really no real reason to choose one over the other, as long as the weapon is a high-status weapon that can apply Corrosive, Heat, and Viral.

Melee

We are looking for a pretty versatile melee weapon that has a moderate attack speed, decent damage, and a decent crit rate/multiplier. Personally, a good choice for this weapon is Broken War (especially since it's a free reward for completing The Second Dream, and comes pre-potatoed!). Another reason to choose this is that a normal attack is guaranteed to proc Impact (in addition to whatever proc(s) you might get from the weapon's normal status chance rolls). As we will see shortly, this will be very useful.

Mod-wise, we will naturally use the [Condition Overload], [Blood Rush], and [Weeping Wounds] synergy, with two elemental damage types thrown in the mix (this is, of course, customizable according to your needs). This is normally quite powerful on its own, and will provide an excellent foundation for madness to ensue. Here is the particular Broken War build I am using as an example.

The Warframe

We obviously want to [Wukong] (duh), but... HOW do we [Wukong]?

The New Abilities

The most powerful (but arguably the most finicky) ability we could inject into this build is Mirage's Eclipse ability, which, even in it's low-powered subsumed state, can provide both a massive damage boost or a decent damage reduction. Here is a brief description of the ability:

1. Your Warframe is in a shadowy area during ability activation
   1. You will gain a maximum of 75% damage reduction. This can be viewed as being applied towards the damage you receive after the armor rating has already been applied.
   2. Combined with the bonus armor from Defy, this will provide a net damage reduction of 96.39%
2. Your Warframe is in a bright area during ability activation
   1. You will gain a large damage boost to all forms of outgoing damage (including melee and ranged damage), and this boost scales with ability strength. Fun!

Since we don't really need Primal [Fury] for this build, we can inject Eclipse in Primal [Fury]'s stead.

Mods

Now that we know what abilities we'll be bringing along, let's get down to the business of choosing which mods we need:

1. Aura
   1. There is only one Aura we really want, and that is Steel Charge, which provides a 60% Melee damage boost. It also is the highest-capacity aura, so it will provide us with 18 extra capacity instead of 14. Coincidentally, the Aura slot is also of the same Madurai (V) polarity as the Aura itself.
2. Mods
   1. The first goal is to maximize ability strength without compromising on ability duration. To this end, we install [Umbral Intensify], [Blind Rage], and [Power Drift] (as well as [Umbral Vitality], to enhance the effect of [Umbral Intensify] from 44% to 55%).
   2. We also wish to Improve ability duration, so we don't have to keep refreshing our Defy and Eclipse buffs. For this, we install [Primed Continuity] and [Constitution].
   3. For survivability, we add in [Umbral Vitality] and [Adaptation] (along with [Umbral Intensify] to enhance the effect of [Umbral Vitality] from 440% to 550%).
   4. To make sure we never run out of energy, we will be using [Primed Flow] to increase the energy maximum, and [Hunter Adrenaline] to gain energy on damage taken to our health.
3. Arcanes
   1. Arcane [Fury] is used, since its 180% melee damage bonus will combine with [Condition Overload] whenever the Arcane procs.
   2. Arcane [Guardian] is used, since it has a chance of improving the armor by an additional 900 points.
   3. Arcane Blade Charger, which has a chance of improving melee damage by 300% after a primary weapon kill, might be able to be used here, but I am not sure if it will be procced by the Celestial Twin. If it is, then it may be a better choice than Arcane [Fury] in certain situations, since it will provide for a better damage boost than Arcane [Fury].

The Stats

Here it is: We can finally reap the rewards of all that thinking by... Doing a bunch of math???

Survivability

Since the melee damage is what we are really excited about, I will save it for last! Here are different calculations for your survivability in a few different scenarios you should expect to encounter easonably often (this assumes you diligently refresh Defy's armor buff, and that [Adaptation] is always running at max!):

1. No Eclipse DR (i.e. every time you use Eclipse as a damage boost), assuming Arcane Guardian proc
   1. Total Armor: 275 (base) + 1,500 (Defy) + 900 (Arcane Guardian) = 2,675
   2. Armor-based DR: 2,675 / (2,675 + 300) = 89.92%
   3. After Adaptation (applied to the remaining 10.08%): (10.08% * 90%) + 89.92% = 98.99% DR
   4. Effective HP: 1,275 / (100% - 98.99%) = 126,437.5
2. No Eclipse DR, no Arcane Guardian proc
   1. Total Armor: 275 + 1,500 = 1,775
   2. Armor-based DR: 1,775 / (1,775 + 300) = 85.54%
   3. After Adaptation: (14.46% * 90%) + 85.54% = 98.55% DR
   4. Effective HP: 1,275 / (100% - 98.55%) = 88,187.5
3. Eclipse DR, no Arcane Guardian proc
   1. Total Armor: 275 + 1,500 = 1,775
   2. Armor-based DR: 1,775 / (1,775 + 300) = 85.54%
   3. After Eclipse DR: (14.46% * 75%) + 85.54% = 96.39%
   4. After Adaptation: (3.61% * 90%) + 96.39% = 99.64%
   5. Effective HP: (1,275 / 100% - 99.64%) = 352,750
4. Eclipse DR, Arcane Guardian proc
   1. Total Armor: 275 + 1,500 + 900 = 2,675
   2. Armor-based DR: 2,675 / (2,675 + 300) = 89.92%
   3. After Eclipse DR: (10.08% * 75%) + 89.92% = 97.48%
   4. After Adaptation: (2.52% * 90%) + 97.48% = 99.75%
   5. Effective HP: 1,275 / (100% - 98.55%) = 505,750 (This is why Arcane [Guardian] is still important!)

Damage

OK, we're finally here! I will be walking through the calculations of the average melee damage, assuming everything is lined up just right. The calculations are progressively organized based on "tier" (elemental damage being lowest, followed by mod- and ability-based damage boosts, followed by critical, followed by viral):

1. Elemental
   1. The base damage of [Broken War] is 187, so the elemental mods provide +180% Radiation damage, and +165% Toxin damage.
   2. This brings the total damage to 187 + (187 180%) + (187 165%) = 832.15
2. Mods and Abilities
   1. We gain 60% damage from [Steel Charge], 180% from Arcane [Fury], 404% from Eclipse, and (8 * 120%) = 960% from [Condition Overload]. This is a total damage boost of 1,604%.
   2. This brings the total damage to 835.15 + (832.15 * 1,604%) = 14,179.84
3. Critical
   1. We have a 304.5% chance of getting a 5.5x damage multiplier. This results in an average damage multiplier of 16.75x.
   2. This brings the total damage to 13,347.69 * 16.75 = 237,476.8
4. Viral
   1. We assume a full stack of 10 viral procs, so we have a 4.25x damage multiplier.
   2. This brings the total damage to 237,476.8 * 4.25 = 1,009,276.41 damage per hit!!!

Since [Broken War] has an attack speed of 1, this directly translates into a DPS of 1,009,276.41.

Key Takeaways (READ THIS!)

This build is primary focused on solo play, in particular for end-game missions. Even though the calculations above are intended to show the extremes of what this build can do, the 1mil melee damage can only occur when you are not gaining any DR from Eclipse, and the 500k effective HP can only occur when you are not gaining any damage from Eclipse. This is simply due to the limitations of Eclipse (again, you gain DR when you activate the ability in shadow, and you gain damage when you activate the ability in light). That said, this build should definitely be capable of taking on any end-game content thrown at you. Besides, even if you do end up kicking the bucket, you've still got three more lives from his Immortal Techniques passive!!!