Edit January 2024: Build is sitting here unchanged for a while now. It's still fine. If you're a veteran player and looking for a speedrun build, this isn't it, maybe I should rename the guide to "Profit-Tanker". World record Profit-Taker was done with a Volt build. Not tested yet: Melee Exposure (arcane) might be able to replace corrosive mods for PT.

• High strength build to boost weapon damage, primarily used to fight the Profit-Taker.
• For Eidolon fights, swap Steel Charge with Dead Eye and use a rank 4 Adaptation. Arcane Nullifier and Momentum are recommended.
• Arcanes: I highly recommend Grace. Bring [Guardian], Barrier or Aegis for extra tankiness; Energize, Avenger, Velocity (and many more) for utility and damage. Mostly personal preference...

I'm not a [Chroma] enthusiast. This is what I usually use for the Orbmother fight...

Playstyle: Keep your 3 (Vex Armor) active, 2 (Elemental Ward) as well if you have spare energy. Kill stuff. Recast 3 before it runs out to preserve the built-up buff strength!

My Weapon / Damage type setup for Profit-Taker:

• Primary: Rubico Prime (viral, heat)
• Secondary: Catchmoon or Tombfinger Crit Kitgun (blast, electric)
• Melee: Redeemer Prime or Zaw (gas, magnetic)
• Arch-Gun: Imperator Vandal (radiation, cold)
• Primary, secondary and melee damage types are optional/replaceable. But since you're actually hitting the fat spider with your Arch-Gun, rad+cold are the best choices here.
• All weapons are replaceable. This setup is what I'm comfortable with and/or have Rivens for. Try weapons with inherent elemental damage, so you won't have to mod for that (e.g. Battacor, Kitguns, Kuva weapons, Plague Zaws).
• Utilizing the Exodia Contagion arcane with a crit Zaw (+ crit Riven) can be extremely powerful.
• Fat spidey is immune to status effects, so there's no reason to mod status chance.

I usually bring a [Smeeta Kavat] for the potential bonus loot buff. Good alternatives are the Adarza Kavat for bonus crit chance or Wyrm sentinel with the Negate mod to avoid that pesky magnetic status effect.

Updates:

• No need to bring an explosive secondary, since self-damage to boost your buffs isn't a thing anymore. I didn't like that playstyle anyway...
• The Hema can still drain your health. If you're fine with this primary weapon, go for it.
• Emissive color doesn't matter anymore.
• If you don't care about your shields (and the armor bonus by shield damage), equip a Decaying Dragon Key (-75% shield). Your damage buff only increases via health damage, so that'll happen sooner and more frequently.
• Adding Necramechs to the mix can further improve your damage output and types.

Elemental Ward

You can hold the ability hotkey of Spectral Scream to switch between elements and respective buffs. (This was originally done by choosing specific emissive colors.)

• Heat: Increases health
• Electric: Increases shields
• Toxin: Increases reload and holster speed
• Cold: Increases armor, reflects incoming damage

Build variation:

Aura:

If you're planning to do Eidolon speedruns you'll probably want/need [Corrosive Projection]. You can use an Aura Forma (not a regular one) to enable any polarity in your aura slot, thus allowing multiple builds to still coexist.

More Duration:

• Option A: Replace Adaptation with Narrow Minded if you're familiar enough with the boss fights to survive without it.
• Option B: If you're willing to sacrifice some range (and maybe strength), you could replace one of the Naramon (-) polarities to use [Narrow Minded] instead of [Constitution] or [Augur Secrets].
  (Keep in mind that you'd need to use a rank 4 Power Drift or Steel Charge for the Eidolon build.)

Optimization and Speedruns:

• Most of the following stuff requires you to be a veteran player who owns primed damage mods, the login reward Zenith rifle, some proper Rivens etc.
• I got tired of squeezing different builds into this setup, so I ended up adding an Umbra Forma and an Aura Forma (not a regular forma). This allows me to swap Steel Charge for Speed Holster and enables more build variations and testing...
• Constitution and Adaptation got replaced by Handspring and Narrow Minded.
• I replaced Arcane [Guardian] with Arcane Velocity to massively buff the damage output of my Tombfinger. Arcane Avenger can give you an overall damage boost.
• Primary: Zenith (gas, cold)
  The Zenith's secondary mode has infinite punch-through, allowing you to kill the shield pylons from any position!
• Secondary: Crit Tombfinger (viral, heat. innate radiation)
• Melee: Dokrahm crit zaw with a Riven and Exodia Contagion (IPS, magnetic, toxin. blast is added by Contagion)
• Missing damage types: Corrosive, electric
• Vigorous Swap can be really powerful. I'd probably somehow squeeze it in instead of Augur Secrets.
• Still testing weapons...and I'm also looking forward to the upcoming Primary/Secondary rework thingy.

Helminth subsume:

Since Spectral Scream is only required for cycling through elements for Elemental Ward, you could replace it with utility stuff like Dispensary, Empower, or anything you like. Replacing Effigy is another valid option. Just keep in mind that Effigy can grant you another Credit multiplier for Profit Taker.

Operator shenanigans:

• Zenurik's Energizing Dash is a great way to improve your energy sustain.
• Madurai grants extra physical and elemental damage.
• Arcanes: Magus Repair (and/or Magus Elevate) is a quick and reliable way to heal up.

There's always some more potential to further minmax, but I like this build and its moderate amount of polarized slots, leaving room for variations and alternative configs.

More Eidolon (beginner's) builds:

Questions? Feel free to message me ingame or via Discord. :)
Warframe tips and beginner's guide here.