I've given Hildryn some time and forma over the weekend and I have to agree with most of the posts in this thread, she needs some serious tweaks. I ran her through a sortie, max level bounties on both Vallis and PoE and lastly ESO. I really love her concept but I never felt like she actually brought anything useful to completing the missions, she was just a platform for carrying my weapons. It's also really frustrating to play her against Grineer and Infested.
Balefire - The launcher is really cool but it's usability drops of really fast with levels. I have dumped a few forma in mine and it's still not even close to as good as many other secondaries which makes pushing the button feel like both an offensive and defensive downgrade. Each shot might cost a bit to much as well.
Shield Pillage - The armor pillage-to-shields at 1:1 is far to low, which is a huge problem. Either way, this really need to work on all types of enemies for Hildryn to feel even remotely OK. It's not cool to have a frame be practically useless against two thirds of the factions in the game.
Haven - I think this is a cool ability visually and conceptually but it does not do enough to warrant it's cost. The shield drains is waaaay to high, the damage is waaaay to low and/or the buff to allies is waaaay to small.
Aegis Storm - Almost exactly the same critique as Haven. I really think it's a super cool ability but it just does not do enough to warrant the cost and risk in using it. The drain is also way to much, especially if the restriction on using Shield Pillage in this mode remains.
I'm pretty sure Hildryn can become super cool with some tweaks, I think conceptually she's awesome - the execution just need some big number tweaks.