She has the wyvern's tail barb fashioned into a dagger; it will produce no new poison on its own, and much of what it had leaked out when she cut it off the beast, but it remains particularly dangerous and will do for the first few times she uses it, and it's possible she will be able to refill it along the grooves through which natural wyvern-venom would have flowed if she finds a kind of poison she'd like to use.
Her mother honors her both with the gift of a new weapon, Lævateinn, and with the opportunity to name her peculiar eight-legged foal that she intends to ride into battle when he is older.
She calls the horse Sleipnir (he's a very cute foal, if... leggy...) and she's thrilled with Lævateinn. It's a glaive... and an axe and a scythe and a spear and a staff and a pitchfork and any other longish melee weapon she can think of; it will change in her hands, its length and blade and weight, as she likes. It is old - well, it's indestructible, and never needs sharpening; it has had every opportunity to become old - and now it is hers. She loves it.
Being an official adult is pleasant in many ways; in others it changes little; and in a few it is wearing and irksome.
But she doesn't mind being able to go along when the frost giants make incursions into territory on Midgard. Odin does not much care about Midgard for its own sake, as far as Loki can tell; she only wants the giants confined to Jotunheim. Loki's motives are different (and would not much matter even if they contradicted outright: princesses are supposed to show up on campaigns of war).
To Loki's immense convenience, the Asgardians outnumber the giants by nearly ten to one and no one she cares about in the least is lethally injured such that she'd feel obliged to mysteriously heal them. The giants are driven away and it is made clear that they are to stop harassing the short-lived people of Midgard.
Loki finds herself charmed by the humans. They're technologically primitive - the Asgardians like a low-tech aesthetic, are rather dominated by this preference, but that's not the same thing. They live and die in, not an eyeblink exactly, but a medium-sized period of time. They keep their souls outside of their bodies and shaped like animals, and the children's can change, which is peculiar but endearing.
The campaign is over in less than a week, and that long only because the frost giants are dug into the mountains. Loki's new toy gets plenty of exercise. She finds it useful to spear it into targets and change it before hauling it out of them, as long as she's not surrounded by many opponents; when she is, she does well to curve her blade for tripping. Her fallback is the favored glaive shape, but Lævateinn's ability to get longer is invaluable against such - well - giant enemies.
They win, the giants leave, the Asgardians prepare to go -
"Mother?" dares Loki. "By your leave I would stay here - no more than a few years. To explore. I am curious about the ways of the mortals and about their world."
"No?" says Fandral. "There are no tales of the invisible warrior sung in the mead-halls?"
"There would need to be an invisible warrior for that," says the stranger. "I am not she."
"If you came all this way to see a Princess of Asgard fight, perhaps you should fight one," says Fandral, grinning at Thor and Loki.
"Perhaps I'm not ready to face such a worthy opponent," says the stranger. "One of their companions, maybe."
"Oh? Who would you challenge, then?"
"The talkative one," the stranger suggests.
Fandral laughs. "Very well then, I accept."
"I seldom beat her," remarks Loki, taking a seat and reducing Lævateinn to a convenient size. "You may have made a strategic error."
"That we shall!" says Fandral.
They draw their swords.
Fandral is quick - but somehow her blows never quite land where she meant them to. Fandral is nimble - but somehow she dodges into a strike as often as out of one. The stranger exhibits no polished techniques, no overtly successful stratagems beyond a gift for feinting convincingly, but somehow things just seem to turn out in her favour, again and again. She is either an unnervingly lucky swordswoman of middling skill, or a master of the art toying with Fandral for inscrutable reasons.
That is very interesting. She should teach a class on Not Being In The Same Place As Pointy Things.
In response, the stranger drops her pretense of mediocrity. Her sword moves with blurring speed and exquisite precision. Fandral holds her own for ten increasingly dramatic seconds, and then the stranger disarms her neatly and stands back.
"I'm really no one famous, you know."
"The way you wield a sword, you should be!"
"Well, that's your opinion," the stranger demurs, but she sounds pleased.
"At least let me see your face so I know what to tell the bards."
"Bards like a mystery."
"Come on! I could almost swear I've heard your voice before..."
"You won't be any happier for knowing," the stranger warns.
"Nonsense!"
"I'll fight you if you tell us your name," Thor offers in an effort to solve this dispute. "You're good enough to be worth a match, without question."
That is not a woman's name. And that is not a woman's face.
"What!" says Fandral, shocked.
"I told you you'd be no happier," he says dryly.
"You lost to a boy," cackles Thor.
"Well - well you promised to fight him!" says Fandral. "Let's see how you laugh after that!"
"...It wouldn't be fair, surely!"
"Is my sword slower because a man's hand wields it? You have seen for yourselves it is not," he says logically. "And you promised."
"You did promise, sister," Loki echoes. "If I say I'll fight him too - and you know I'm nearly certain to lose - will that spread your embarrassment around sufficiently?"
"...fine," grumbles Thor. She hefts her mace (Mjolnir is best left out of the practice halls). "Come and try your skill against a princess, boy."
Against Thor, the competition is much more even. His effort is obvious, and so is the outcome; he scores a few good hits, more than most people can manage against Thor, but eventually loses.
"I won't give you as good a workout as she will," Loki says, rolling to her feet and expanding Lævateinn into a scythe. "But it'll be different. If you're game."
Perhaps to avoid ending the match too early, he doesn't put in the same level of effort that he did against her sister. But he is still very, very good.