Personally, I prefer the air!

Steel Path and General Use Hildryn Prime build with lots of utility and just enough strength to fully strip armor and shields in 2-3 casts of |2| Pillage. Every other build I see on here focuses on getting to the minimum power needed to fully strip armor and shields in just one cast of |2| Pillage and subsuming something over her |4| Aegis Storm, but in doing that, you lose a lot of what makes [Hildryn] fun in my opinion. (Granted, I too was running Elemental Ward over Aegis Storm until Update 37.0 where DE changed it so that Pillage can be cast during the ability, which gave me the idea for this build in the first place!) You're mashing |2| anyway, so this build focuses on using all of [Hildryn]'s base abilities in tandem. We reduce power strength a bit to add more range, which feels better for |4| Aegis Storm and |3| Haven + the [Blazing Pillage] Augment.

The playstyle here isn't much different from other [Hildryn] builds:
1. Activate |3| Haven to start proccing heat statuses with Blazing Pillage and dealing some AOE damage.
2. Activate |4| Aegis Storm to deal even more AOE damage and provide some much-needed hard CC.
3. Make sure |1| Balefire is active. (It should be once you activate |4| Aegis Storm now, but I've had some bugs with that).
4. Mash |2| Pillage essentially every time that you can because that's how you strip armor and shields, and keep restoring your shields.
5. In between casts of |2| Pillage, annihilate everything else with an aerial bombardment of shots from |1| Balefire. (Embrace the B-52 Bomber that you are now).

Most other build rely on [Adaptation] for survivability, but in mine, we're using [Aerodynamic], [Aviator] and the Boreal Set Bonus with [Boreal's Hatred] to have constant DR while in Aegis Storm, which is what you'll be in most of the time anyway. I run a polearm with [Boreal's Contempt] to get the set bonus up to 40% instead of just 20% with only [Boreal's Hatred]. I've only really tested this in Steel Path and it works fantastically on 90% of missions. Obviously don't take [Hildryn] into any infested missions, as they don't have armor or shields to strip and replenish your own shields, plus the prevalence of toxin statuses and damage makes it very hard to survive. I also found Excavation to be a little difficult because she doesn't really [Protect] the excavator. This probably works well for Endurance Steel Path, but your damage will definitely fall off before level 1000 enemies, which'll make it harder to deal with overguarded enemies; I haven't tested it so I don't really know.

• You could probably run an [Adaptation] build if you really wanted to, just swap out [Boreal's Hatred] for [Adaptation] and change [Aerodynamic] and [Aviator] to
  something else, as they do not stack with [Adaptation]. (Again, I just feel like those mods provide a more consistent form of DR than [Adaptation])

For Arcanes, I'd definitely stick with Arcane Barrier and Molt Augmented as those will benefit you the most, but an argument can definitely be made for like Arcane Aegis or others similar to that.

As for Archon shards, I personally like 2 regular or 1 Tauforged Amber Cast Speed Shard(s), and 3-4 regular or Tauforged Crimson Strength Shards. I would only use Azure Shards if you don't have enough shards yet to fill up all the slots, and [Hildryn] doesn't really benefit from the combined shards: Violet, Topaz and Emerald.

Your loadout is pretty flexible to however you wanna play, sure there are meta picks and you can totally min-max and pick everything based on how it functions with the build, like a Sentinel or Moa would be perfect with the [Guardian] Mod, but I typically run my [Smeeta Kavat], because I'm a loot goblin and I like extra loot, plus the crit buff feels amazing with |1| Balefire. As stated before though, I do highly recommend using any polearm with the [Boreal's Contempt] mod to increase the set bonus from 20% to 40%. The [Balefire Charger Prime] build I use is ninjase's. My polearm build is this here.

Falco's personal favorite [Hildryn Prime] build