This is a standard Viral Electric [Phantasma] build which is best used for general use and against groups of enemies, as electric procs have a small AOE (3m), are uncapped and scale with elemental mods. Armor strip helps against higher level Steel path grineer/corrupted enemies.

Heat is an alternative option which scales higher against single targets and can benefit from Heat inherit mechanics. Simply swap [Primed Charged Shell] for Incendiary Coat.
If you plan on using a Viral Primer, swap the viral mods for Shell Shock + Vigilante Armaments.

Mod Breakdown

• [Galvanized Savvy] : Gives +80% damage per status effect. [Phantasma] procs impact, radiation, electric and viral giving a maximum of +320% dmg without external priming. Also gives +80% status which is essential for status effects, the key damaging component of phantasma, but is additive to Primary Merciless.
• [Galvanized Hell]: Gives +230% multishot at max stacks.Multishot is essential on beam weapons as it increases both beam damage and status chance thereby basically double dipping in the damage of status effects (such as electric).
• Viral ([Toxic Barrage] and [Frigid Blast]): viral status boosts damage of electric procs by up to 4.25x at 10 stacks. You want to use maxed mods for the bonus to status chance.
• Electric ([Primed Charged Shell]): this is the key damaging elemental mod giving +165% electric damage to each electric proc and increasing electric bias
• Primed cleanse grineer/corrupted: this double dips on status effects, multiplying the damage of electric procs by +140.25% (i.e. 2.4x). Ths is flexible for vigilante armaments or magnetic strafe if you dislike faction mods.
• Shotgun Barrage/Repeater Clip: firerate directly multiplies DPS by 1.9 to 2.05x.
• [Shotgun Elementalist]: boosts status damage by 90% and also increases clip size which is a nice bonus.

Exilus:
Personal preference but [Phantasma] can be an ammo hog. Use primed ammo mutation if you feel ammo is an issue.
Otherwise leave the default polarity and use Galvanized Acceleration.

Arcane

• Shotgun Vendetta: +180% multishot is better than merciless after only 2 status effects due to how multishot double dips status damage, however is only better than deadhead with headshots after 6 statuses (i.e. using an external primer). Use this if you aren't planning on aiming at heads or not using electric.
• Primary Deadhead : The bonus 1.3x headshot multiplier double dips when electric procs hit the head, dealing 1.69x damage (note elec procs no longer double dip the usual 3x headshot multiplier and instead have a base multiuplier of 1x). Use this is you are planning on aiming at heads AND using electric.
• Primary Merciless : Fine alternative when not aiming at heads.

ELEMENTAL VARIATIONS

• Heat: Great for single target as heat procs constantly refresh the duration of all previous heat procs meaning it can stack infinitely. Simply swap the two electric mods for [Incendiary Coat] and either [Blaze] or [Scattering Inferno]. Can also work with heat inherit but you don't really get much additional DPS out of it unless you drop both virals and one heat mod for crit mods + vigilante armaments.
• Toxin: Optional for steel path corpus as electric works fine too, but toxin completely bypasses shields. Simply swap out electric mod for toxin mods and cold mod for [Vigilante Armaments]. Works well with expedite suffering.

quick video showcase:

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