This is a dear subject to me so I wanted to try to cover everything.
The vital importance of Harle the enigmatic jester has been one that has gone somewhat under the radar. Is she an antagonist or not?
The main point of my theory is that she is not actually a villain at all. She is a tragic puppet that gave her all trying to protect the one she loved despite the strings holding her back.
One thing you learn right off is that there is one person she hates more than anyone and it shows in every interaction with her. That person is Kid. But that leads us to asking why she hates Kid so much. Haven't they only just met?
One could easily say it's because Harle obviously likes Serge for some reason and just sees Kid as a competitor for his affection, but I believe there is much more to it than that.
From what's implied about her, Harle has some very impressive abilities and she knows far more than she lets on. This seems to point to her having the ability to move between the dimensions and see what's on the other side. Just like when she follows Serge when he's dumped into an alternate world in his new Lynx body. She learned more and more about Serge and fell in love with him. But she also learned something else.
I believe this thing is the real source of her hatred for Kid. A hatred that causes her to antagonize Kid and even urge that she be left to die even though it causes Serge himself to think badly of her.
Watching these timelines, it became apparent that if he lives Serge is fated to meet Kid, become interested in her, and be led every time to danger and even to his own death. This is why Harle will go out of her way to protect and help Serge while pleading with him to part ways with Kid.
Her vitriol for Kid comes from witnessing the timelines in which Kid has been the cause of suffering and death for Serge. It's even evidenced in even her final moments when Kid is about to destroy everything with the flame. Harle, despite having just been injured, looks up at Serge before leaping to her feet and lashing out at Kid. Telling her that she doesn't care if Kid destroys herself but she won't let her drag Serge down with her. With the flame in her hands, she is almost immediately taken to be absorbed by the Dragon God, but not before protecting Serge.
Well, if she loves Serge so much, why does she still help Lynx? I honestly believe she has no control over this. She was created in secret by the dragons when they got hold of some human genetic material (Most likely from Schala or Kid. Though purposefully disguised by her clothes and makeup, Harle is nearly physically identical to Kid). They combined it with the DNA of the seventh dragon god to create a new being and tasked her with gaining Lynx's confidence and stealing the frozen flame from him. Because of this link to her creators, I believe she is physically unable to deviate very far from their will without risking her own destruction.
She was only able to accompany Serge later in the game because he had Lynx's physical form. It created a loophole for her to exploit and she was able to help him as best she could. Unfortunately, Serge wanted to pursue Lynx to a place Harle knew was dangerous. If he went there, she knew she would be forced to betray him and steal the flame so she did the only thing she could think of. This was the moment Starky caught her crying on the ship.
She ran away, but still kept watch over Serge as he chased after Lynx, probably hoping that if she wasn't there, then she wouldn't be forced to act against him. But the situation worsened due to Kid's actions, and Harle had no choice but to reveal herself to intervene. Even if it meant handing over the flame to the Dragon God, she would rather do that and essentially die than allow Kid to outright destroy Serge along with the rest of the world.
EDIT: One connection worthy of note that I wanted to make here. It's tenuous, but I do believe Harle has some connection the talking mirror in Radical Dreamers, just as FATE-Lynx seems like an expy of the spirit of RD Lynx without actually being the same person. (unless he is and somehow RD Serge doesn't know what his own father looks like)
The mirror is never hostile to Serge. Only Kid. There was even a mistranslation in one of their interactions. In the incorrect version, the mirror offers to take Serge into the mirror if he touches it but then she refuses to save him at the last moment from being trapped inside. In the original, it's Kid she tries to coerce into the mirror. But unexpectedly Kid tried to force Serge do it instead and the mirror chose to break itself rather than harm him. These actions are eerily similar to Harle's behaviour with Serge. Enigmatic, but immediately devoted to Serge and his safety, coupled with an intense hatred for Kid.
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The Chrono Trigger/Cross/Radical Dreamers Connection
Be forewarned, some of this is speculation, but based as much as possible on in-game dialogue and other facts.