Why?

[Reactive Storm] makes [Baruuk] really, really fun to play by morphing his ult Serene Storm into a Weapon of Mass Destruction.
Since we need [Baruuk] to be really angry to use his ult, we need to erode his Restraint as fast as possible.

We have, like, 3 different ways to erode his Restraint by using Elude to dodge attacks, Lull to calm nearby enemies and Desolate Hands to launch explosive daggers.
Elude needs incoming enemy attacks but less reliable due to Warframe enemy AI (Artificial Idiots, I guess).
Desolate Hands is fixed at 1 dagger per second.
So Lull became the only viable option. Since Lull can't recast while active, we need its duration as low as possible.
Here's the fun part: Ability Duration only affects Elude and Lull, and we literally don't need Elude so much, this makes low duration have no downside at all.

Let's expoit that, shall we?

How?

Obviously, [Fleeting Expertise] and [Transient Fortitude]. Low duration with extra Efficiency and Strength, nice.
[Augur Secrets] for extra Strength. [Augur Reach] instead of [Stretch] because at 130% range Lull field is big enough, and we don't want too much range which will make Desolate Hands daggers (our 90% damage reduction) harder to maintain.
[Reactive Storm] of course, and [Vitality] + Adaptation to make Baruuk even more tanky.

And that's 7 mod slots taken. Aura doesn't have so many choices with a - polarity. And I choose more Strength for the last 2 slots.
That's just 2 formas.

Which mods are swappable?

[Vitality]: [Umbral Vitality] + [Umbral Intensify] with or without other Strength mods are fine too of course, but that needs even more forma.
[Adaptation]: [Quick Thinking] is also ok for this slot since [Baruuk] have 300 energy unmodded. [Rolling Guard] is easier to obtain but less effective due to some undocumented bug feature of Desolate Hands and status procs.
[Blind Rage]: 105% efficiency is ok I guess, but [Energy Conversion] is also a viable choice, less Strength but much more efficiency for Lull spamming.
Exilus Slot: I prefer [Primed Sure Footed] If I HAVE ONE!

Anything else?

Just spam Lull around enemies for his ult, and remember to recast Desolate Hands when dagger count is less than 9. That's all.
For his [Desert Wind], just avoid Impact mods beacuse it have little to no effect when using [Reactive Storm].

It is truly awkward for this warframe because if you actually grinded your way towards him, you probably have many more better choices than him already. And if you are new to this game, you have ZERO reasons to buy him with Platinum unless you are too rich. And he's ugly af with only one alternative ugly helmet I have to buy a Tennogen to compensate for my eyes

But he's really fun to play atm.