3. Rosa (Final Fantasy IV)
The call to badassery can come at any time and Rosa answers hers when her king turns out to be batshit insane (or an imposter or whatever). When Cecil is branded a traitor, she takes up her bow and leaves her imperial capital to seek him out. While Cecil watches the world pass under him from atop an airship, Rosa crosses mountains and deserts alone, on foot to warn Cecil that he's a wanted fugitive. That's right. The protagonist has a personal airship, a summoner's aid, and half a sparkly vampire's worth of brooding on his short stroll through the nearest town. Meanwhile, Rosa gives up a steampunk aristocracy to walk halfway around the world.
2. Marle (Chrono Trigger)
Princess Nadia of Guardia Kingdom nicely fits the "rebellious princess" trope, as she's stifled by her overprotective father and smothered by the duties of royalty. Sneaking out under the pseudonym Marle for a day of fun at the Millennial Fair results in a trip through a time portal to the Middle Ages. While that's the kind of thing that would have most people crawling into a padded closet, Marle steps right into the adventure armed with a crossbow and an invincible optimism. Post-apocalyptic wasteland? Ooh, let's check it out! Ancient space parasite? I'll bet we can fix that! Prehistoric dino-queen? Let's be friends! Marle is brash, even reckless, but not because she doesn't understand danger, it's because she knows that she can handle it.
1. Sun Lian (Jade Empire)
The princess of the Jade Empire in well Jade Empire watches her once respected father make several questionable changes to the kingdom. She investigates the apparently corrupt influence of a man called Death's Hand (and really, who wouldn't trust someone with a name like that) using her wealth and influence each day at court. With enough evidence, she wanders into the night, under the mantle of Silk Fox like a Far East Lady Batman. Sun Lian needs rescuing, but her real prison is her own mind. She isn't naïve, but she's so certain of her father's innocence that she can't be convinced there can be any evil in him. She's more held back by her own short-sightedness than anything else. On the other hand: Lady Batman.
I rest my case.