DON'T USE CHARGE SHOT, USE QUICK SHOT

Quick shots consumes 22% the shields that charged shots do, but deals half the damage

Not to mention Balefire shoots faster when not charging shots.

[Overview] & Theory

This is a funky build, not like what you'd usually put on a weapon.
[Balefire Charger] (Prime) has pisslow crit stats and horrible status chance, so we're building for damage bonuses only.
Primed Fulmination is an exception to this rule, as it exponentially increases the explosion radius w/ ability range.
[Galvanized Diffusion], [Hornet Strike], [Lethal Torrent], & Expel are your basic secondary damage mods, boosting average damage in 3 stats and burst damage in 4.

Element Choices

Element modding for the [Balefire Charger] is a unique challenge, but a necessary one. Using "one size fits all" builds are a huge damage loss no matter the circumstances.
Element choice is not only dictated by the faction you're facing, but also if your [Hildryn Prime] build fullstrips enemies with Pillage.
Another thing that throws a wrench into our plans is the innate Electricity damage. This means we can't have a basic element without a combo element that uses Electricity.
I've written a short guide you can take a peek at to find the optimlal elements for all factions + [Hildryn] builds.

Grineer

Viral + Electricity ([Magnum Force] is better than [Convulsion] here, but it absolutely cannot fit.)

Corpus

Viral + Electricity (")

Infested

Hildryn simply cannot play into Infested units, as they don't have shields or armor to convert into over/shields with Pillage.

Corrupted

Corrosive + Heat