At the start, the Warrior of Light will meet up with Ryne and Gaia and catch up with them. Ryne will reveal that things in the Empty have taken a turn for the worse—when we arrive there to see what she means, we'll discover that snow and ice have overtaken all signs of life and activity at the campsite—a result of Ice aether running rampant.
Ryne takes responsibility for this, suggesting it's due to her failure to control Shiva. But rather than immediately rush to fix things, she, Gaia, and the Warrior of Light will discuss what, exactly, the problem with Shiva was. Multiple angles will be examined, from Ryne's lack of the Echo, to the lack of an external controller on the primal's aether levels, to a slavish devotion to "accurate primals" over "primals that will do what we need".
Finally, Gaia will present a solution: They summon an original primal embodying all elements at once (think Bahamut), with herself serving as the vessel. Ryne is opposed, not wanting to risk Gaia's life, but Gaia talks her into it. And so we go along with Gaia's plan, with all three heroes contributing to the "idea" of the new primal to be summoned.
BOSS 1: Heritor of Chaos - Griever
Music: Maybe I'm A Lion remix
Gaia, as it turns out, doesn't so much control Griever as keep it from running wild. But she does manage that, and with her and Ryne's help we slay the primal, releasing its aether out into the Empty. Gaia remains inside Eden to catch her breath—the fight has taken a lot out of her. Ryne and the Warrior of Light head outside to check on their handiwork, and Ryne is delighted to see that life has not only returned to the campsite, but is actually spreading—flowers are in bloom and such, and the area that's alive is much larger than before.
And then they hear a scream over their linkpearls—speaking of which, they really ought to have some—and rush back into Eden just in time to catch an Ascian seizing control of Gaia's body, not unlike how Lahabrea took over Thancred's long ago. The Ascian reveals herself to be Altima, and thanks the duo for giving her the chance to seize one of her missing fragments—Gaia's soul is a part of her own, in other words. The origin of Gaia's name is also revealed here: Much like Emet-Selch, Altima is the title of her office and her true name is Gaia.
She uses Eden to draw forth a massive amount of aether from the land, then uses that aether to tear open a voidgate in the sky, allowing the voidsent Erebos (see: Eden's Gate fight vs. the Voidwalker) into the First. The Warrior of Light has to fight it off.
Boss 2: Primordial Voidsent - Erebos
Music: Same old Force Your Way remix
While we were fighting Erebos, Ryne was fighting with Altima. She managed to drive her deeper into Eden, but was unable to defeat her or free Gaia from her control. Ryne brings up the possibility of summoning a primal to give them a better chance against her, but is also worried that it'll run wild the way Griever and Shiva did. The Warrior of Light reassures her, and Ryne bids us go after Altima while she prepares.
Boss 3: Oracle of Darkness - Altima
Music: A remix/original song, akin to Return to Oblivion, but possibly based on one of the songs associated with the Ascians Tomorrow and Tomorrow remix, maybe?
Despite her appearance and "title", it's Altima in control of Gaia here. But after we've defeated her in combat, Shiva in Hydaelyn form arrives on the scene and attempts to forcibly separate Altima from Gaia. Given her appearance and behavior, it's clear that Ryne is acting as her vessel—and that she seems to have gotten the summoning down right this time. Even though she's not in control, Shiva is acting along the lines of Ryne's own wishes and beliefs.
Though she's able to destroy the means by which Altima is controlling Gaia's body, Altima has one last trick up her sleeve: She transforms in a similar fashion to Emet-Selch "becoming" Hades or Lahabrea and Igeyorhm fusing to become Ascian Prime. Gaia is unwillingly absorbed into this new form, and though she's desperately fighting off Altima's will from the inside, it's only a matter of time before she's forcibly rejoined into the Ascian.
Boss 4: ??? - Gaia
Music: The Extreme remix
This boss will resemble Ultimecia's final form in FF8, but with Altima as the top half and Gaia as the bottom half. Shiva (Hydaelyn) will also carry over into this fight, assisting us in trying to save Gaia while defeating Altima. Once the fight's over and Altima's on the verge of true death, she'll let go and allow herself to be absorbed into Gaia, becoming one with the girl's soul instead of the other way around. Shiva (Hydaelyn) will also dissipate herself, content that she has served her purpose.
After the fact, Ryne will reveal that Eden itself helped guide the process of summoning Shiva—her goal of teaching Eden how to manage the Empty without her was a success as well. With the threat to their world gone and Eden able to carry out the work unaided, she accepts this as proof that her duty as the Oracle of Light is over and resolves to travel to the Source alongside Gaia in the future.