Beatrix: "You are no match for me! Ignorant fools."
What very quickly becomes apparently during the Beatrix battles is that her words - prideful and arrogant as they might sound, especially when combined with the devastating hair flip - aren't empty threats. Beatrix isn't a hapless or comedic villain who brags about their prowess and postures with no actual skills to back up their boasting. Every single fight against Beatrix is unbeatable. Once you reduce her HP enough, she'll pull out one of her impressive Seiken (Holy Sword) moves that completely incapacitates the entire party. Zidane, Freya, Quina and Vivi are absolutely no match for her.
Beatrix: "How ridiculously weak... Isn't there anyone who is worthy of facing me?"
It suggests that it's been a long time since Beatrix has been bested in battle. The fight with Zidane seems to have almost bored her. It makes the little bit of trivia about Steiner besting her when she was 17 all the more interesting. Was that the last time she lost a battle? Does she wear an eyepatch due to injuries sustained in this battle? And, while we're speculating, Freya's long lost love, Sir Fratley, is later encountered in Cleyra. But he has completely lost his memories. We don't ever get an explanation for this, but we do know that one of Fratley's goals was to challenge Beatrix in battle. It would be interesting to know if that fight ever took place and if it is at all related to his memory loss...but alas, it's only something we can speculate on.
With Zidane and his friends defeated, Brahne leaves Burmecia to prepare to attack Cleyra. Beatrix, of course, goes where her Queen goes and leaves with her. Zidane, Freya, Vivi and Quina are left lying in the destruction of Burmecia, while the rain continues to fall.
Cleyra is an interesting place. It's also my favourite location in Final Fantasy IX - and this is an expansive world with a lot of unique and colourful areas to visit. Cleyra and its tragedy also marks something of a turning point in the game for me. Things so far have been dark - there has been death and destruction and a monarch hellbent on war, after all. But the events of Cleyra not only bring the death and destruction to another level, it also begins to talk about the so far mysterious Eidolons and answer questions about Brahne's goals.
Situated not far from Burmecia, the Cleyra settlement sits in a giant tree and is surrounded by a sandstorm that protects it from the outside world. The people of Cleyra were originally from Burmecia, but they broke away and formed their own settlement after disagreeing with Burmecia's growing taste for war. The settlement remained in isolation ever since. They have a unique and peaceful culture, and no army to protect themselves. This is a pacifist nation. Cleyra has has some very pretty music. To reach the settlement, one needs to travel up through the trunk of the massive tree.
The settlement itself is beautiful. Zidane manages to arrive before the Alexandrians and finds that some Burmecians safely made it to Cleyra - including the King. In an effort to boost the sandstorm - their protection against outside forces - the Cleyrans and Freya perform a a Ritual Dance, which is a prayer to strengthen the storm. The storm itself is powered by a sacred jewel that sits in a harp played by one of the Cleyrans during the Ritual Dance. However, the strings of the harp shatter at the end of the dance, and the sandstorm fails. Cleyra is left vulnerable.
Thinking that the loss of the sandstorm will allow Alexandria to attack Cleyra by sending soldiers up through the trunk, Zidane and Freya take their companions and head downwards in the hope of stopping them. However, they find only a few soldiers and Freya realises that this can't be the true force - this is a distraction. We have this confirmed by Beatrix, who appears in the trunk right after Zidane and Freya return to Cleyra.
Beatrix: "Ha! They fell for it."
Back in the settlement, Beatrix's soldiers are attacking, alongside black mages who are warping in from the Red Rose - Queen Brahne's airship that hovers nearby. Zidane rescues what people he can and they take refuge in Cleyra's cathedral. However, Beatrix swoops in - literally, as far as I can tell - and takes the jewel that was contained in the harp in a very dramatic fashion.
Cleyran High Priest: "Eek! Have mercy!"
Beatrix: "Hmph! Pathetic rodents! You fail to grasp the true power of this jewel!"
The jewel is what the Queen wanted. With that in hand, Beatrix dashes out of the cathedral. She has no reason now to linger in Cleyra. However, Zidane is hot on her heels.
Zidane: "Think you can get away?"
Beatrix: "Get away? Hahaha. You're a bigger fool than I imagined... Have you forgotten how badly I beat you back in Burmecia?"
Freya: "So, you are more the fool for not finishing what you started!"
Vivi: "You're gonna pay!"
Quina: "I find no tasties in this town, so we cook you for breakfast!"
Beatrix: "Then allow me to shatter your delusions of grandeur."
The smack talk from Zidane and co. is admirable but really? How quickly they forget an ass kicking. It's interesting that Beatrix straight up ignored all of them until they challenged her. She obviously sees them as no threat to her and didn't have any plans to engage them - as far as Beatrix is concerned, there's no point. They're not worth her notice. However, once challenged, she doesn't back down. This begins the second unwinnable fight against Beatrix.
This plays out exactly the same as the last battle - you whittle down her HP until she grows bored of this and uses a finishing move to incapacitate your party and end the battle.
Her work here concluded, Beatrix orders the black mages to return to the Red Rose. They begin to teleport out of the area, with Beatrix jumping into one of the teleport portals to leave with them. Zidane, Freya, and Vivi also make use of these (while Quina decides to leave on foot), and teleport to the Red Rose shortly after Beatrix.
As they do this, the sky turns red, and a hole appears above Cleyra. A rider on a horse wielding a spear begins to descend. Queen Brahne has summoned the Eidolon Odin.
Odin entirely obliterates Cleyra, killing anyone who remained in the settlement. Despite the fact that the Queen got what she came for - this precious jewel - and that the Cleyrans posed absolutely no threat to her, she literally wipes them from the face of the planet with this unimaginable power. Only a charred stump of the once huge tree remains to indicate Cleyra was ever there at all.