My observations probably echo everyone else's, so I'll try to be brief:
(Un?)Surprisingly squishy. I guess it should've been expected for a shield tank that also uses her shield as energy, seeing as how shields have long been a joke in this game (and then we're using our precious shields up for our abilities and getting nothing defensive in return? Hmmm...) Are we expected to put vitality on alongside redirection and fast deflection to counteract toxin/bleed damage? I don't even need to point out that we don't have the mod space for that. The time it takes for her #2 to return shield is way too long, too.
Very clunky. The worst is casting #4 then #1, but then using #1 outside of #4 is slow for no apparent reason. Her #2 once again takes way too long to affect her shields.
Shield management: Just because she's the first warframe to use shields in place of energy doesn't mean you need to go nuts with draining ungodly amounts of it whenever possible. Her #3 may as well just have the "drains own shields" effect listed in its ability summary because that's all it's useful for. Her #2 takes so long to return shielding, even if you immediately return the 'wave', I'm not even sure it's worth exposing myself in LoS of enough enemies to regain significant shielding, considering that they'll all be shooting at me. So far I've found it better to just hide in a corner and let shield regen do its job because the #2 ability does not. Hiding for shield regen to kick in is actually only about as annoying as pressing 2 every 2 seconds so it's not any worse, and since I actually regenerate shields by doing so it's even better!
Lastly I want to point out this: Garuda isn't meant to be a tank, but she's far tankier than Hildryn even while consuming all her HP to fuel her abilities just because she can do CONSTANT health regeneration. Hildryn first of all needs to ignore ALL damage to HP while shields are up instead of just while under overshield because she consumes her shield (and thus overshield) to power her abilties, making the current method of HP invuln useless. Second of all she needs some way to constantly regen shielding. Preferably some way that doesn't involve mashing the 2 button every 2 seconds (old Nekros style?) The shoulder shields that come out during Aegis and her dash also seem cool, so even though I know it's probably already too late to make this recommendation I would like to recommend that Hildryn gain passive "shield plates" as she consumes shields to feed her powers. Completely invulnerable plates that progressively appear across her body the lower her actual shield gets, temporarily reducing her vulnerabilities instead of increasing them as currently happens. They would persist for a set time instead of disappearing with shield regen. This would reward Hildryn for using powers instead of punishing her as it does now, and once shields are depleted and the 3 second invuln drops she'll still have decent protection while trying to regain shielding, possibly without having to hide.
Edit: Oh and her launcher. I have Gunslinger AND Anemic Agility on to make the charge speed bearable and it's still absolutely useless once the nullifiers start becoming prominent in the Corpus crowd. It underperforms in every way compared to a Staticor and it consumes your shields to do so.