Written in Update 31
Garuda is one of those Warframes who, for all her sass, was underutilized in her early days due to her original skill kit emphasizing "high risk, high reward" gameplay, and yet the rewards were, well, not rewarding enough - she had to always keep her HP low to augment her damage output via her old Death's Gate passive, which was rather counterintuitive as she is also meant to be an offensive healer. Plus she had to depend heavily on her signature 
Blood Altars for survivability, which, frankly, limited her offensive options as she has to place, replace and stay close to them. And when she deliberately dropped her HP to gain higher damage, a lucky 
Slash or 
Toxin proc - the latter bypassing her supposed safeguard with 
Dread Mirror - was all that enemies needed to stop her in her tracks. She is ought to be a calculating gore queen, and unfortunately, the calculating part overtook her supposed lust for blood.
Then came one of the biggest boons for Garuda players (I still consider myself a 
Saryn main, but Garuda's sass has her charms) and, poetic enough, it requires a blood sacrifice: 
Sevagoth, so that Helminth can extract the extremely versatile 
Gloom to infuse into other Warframes. Replacing Blood Altar with Gloom finally gave Garuda (some would refer to her as "Gloomda") the mobility she needs to keep goring enemies with her talons while still maintaining her unique role as a highly offensive healer. And, best of all, Gloom synergizes extremely well with Garuda's own 
Bloodletting, as she can keep sustaining the aura by slashing off her own HP - which she can easily replace by goring a nearby enemy, anyway.
Plus, she can use Bloodletting for another purpose...
The Cannoneer Build
- Aura:
Steel Charge, Growing Power or Rifle Amp - Exilus: Cunning Drift
- Warframe Mod List: Umbral Intensify, Umbral Vitality, Adaptation, Primed Flow, Blind Rage, Stretch, Blood Forge, Quick Thinking
- Minimum Forma requirements: Two Umbra Forma and one standard Forma (note that this is true for Garuda Prime; for standard Garuda, you need one more Forma for )
- Skillset:
- Dread Mirror, her most reliable directional survival option, especially against Nullifier snipers.
- Gloom, replacing Blood Altar to transform herself into a mobile healer and crowd controller.
- Bloodletting, to quickly replenish Energy for keeping Gloom powered up, as well as to quickly reload guns.
- Seeking Talons, to force Slash procs on enemies, smashing them later on with True damage.
- Weapon Options:
- Kuva Zarr, the primary reason this build is named "Cannoneer".
- Tenet Envoy
- Tenet Arca Plasmor
- Prisma Angstrum as an equally explosive sidearm.
- Kuva Grattler or Kuva Ayanga as a slow reloading heavy "sidearm" - which can also be reloaded quickly by Blood Forge.
- Any other weapon known for being a pain to reload, but preferably high explosive, high magazine capacity weapons.
Explaining the build
The above mod build emphasizes a balance between effective crowd control and dishing out a lot of pain (more on that later) by sacrificing Ability Efficiency for Strength and Range. Because Gloom's maximum drain per second, determined by Efficiency and not Duration, is capped at ten nearby enemies and remains the same even if there are hundreds within its aura, Garuda's energy reserves is not going to be quickly drained even if Blind Rage kneecaps her Efficiency stats. She can always quickly replenish Energy more reliably with Bloodletting anyway (the risk of getting downed by a lucky shot while she's twirling is offset by Quick Thinking) and it's a far more economical option than, say, equipping 
Hunter Adrenaline and taking damage - which will only be hampered by triggering Adaptation or deploying Dread Mirror.
And since she's going to be using Bloodletting a lot anyway, we might as well use it to push DPS potential further by equipping Blood Forge and then letting her Kuva Zarr or Tenet Envoy constantly spit out rains of death without the momentary pauses caused by manually reloading these weapons - this is much more pronounced in the Zarr's case, with the need to reload the gun one shot at a time. And with the reworked Death's Gate passive now simply requiring that Garuda kills anyone to buff up and maintain additional damage, imagine how much pain her guns constantly push out.
The above build is tested solo on favorite Steel Path Survival missions such as Elara, and Garuda and her guns made short work of mob waves and even luckless Acolytes. If there are moments of danger for her, it will be those, yes, annoying Nullifier Crews who can make your shots bounce back at you and stagger you, snipe you from a safe distance and, most importantly, blatantly disable your Gloom if they get too close.
And I have not even touched the topic about her 
Talons yet.
An alternative build
But of course, some Garuda aficionados would rather use weapons such as the 
Nataruk, 
Lenz or 
Kuva Tonkor, which would not really benefit from Blood Forge as they sport single-ammo magazines. In such cases, you can simply replace Blood Forge with Umbral Fiber for the set's synergy (and to give 
Garuda Prime an added oomph, given her higher Armor stat over her standard counterpart). And if you really feel confident, you can replace Quick Thinking with something else.
Big baddie hunt potential
Note that with Garuda's passive rework, maximizing her damage potential requires that a lot of enemies be sacrificed with regularity. So, oddly enough, she tends to dish out less damage against bosses who don't have swarms of reinforcements with them. And the most notable perhaps of this case is going be the Eidolons and their Vomvalyst support, the latter not counting as a Garuda 'kill' when they're either absorbed by an Eidolon Lure or finished off via the Operator mode. (She will have better fun against Profit-Taker and her constant swarms of goons, on the other hand).
To try to keep up with her damage potential, and given that most would bring sniper rifles such as 
Rubico Prime to an Eidolon hunt, a high explosive sidearm such as 
Prisma Angstrum can help keep her damage buff up by quickly taking out nearby Grineer camps or, not minding protests from The Business, wildlife. The Gloom and Bloodletting combo still helps greatly with managing Vomvalyst swarms, particularly when they're attempting to approach the Eidolon to heal.
Conclusion
Few can beat Garuda's sass... unless you use her Noble Animation Set on Saryn
Garuda is arguably one of the sassiest, if hubristic, Warframes out there, and Sevagoth's arrival and her recent rework have finally given her her much needed limelight to show everyone why she is the Crimson Maiden of Death. This does come at the cost of her iconic Blood Altars, which can possibly be addressed by granting it an added passive effect besides healing and/or a well thought out ability mod.
But for now, it is high time for the gore queen to reassert her dominion.