It's been a good day of training - hard, but good, in the way that leaves your muscles aching pleasantly and you know you'll really feel it tomorrow but for now you're just content with your progress. A few hours of training with axes, running Papyrus through his paces, then wrestling with Greater Dog until he finally went down for a nap. You're covered in bruises and sweat (and possibly tomato paste), grimy and satisfied, and once everything is taken care of for the day, you head back to Waterfall to cool down and clean up.
One swim later your hair is soaked and plastered against your skin, but your scales are clean again and you feel plenty hydrated. You throw your clothes back on carelessly - they're gonna get soaked again anyways, right? - and then you're ready to start your hunt for swords. Sometimes they fall down from the surface; some are new, but lots of them are old, and in any case most monsters besides you don't actually care about them. But sometimes the humans have cool stuff, so you like to spend an hour or two searching and sifting through garbage at the top of the waterfall before you head home.
Forty minutes later, you haven't found anything good, so you're ready to call it quits when you spot a little ball of yellow and white on the rope bridges down below.
No monster looks like that in Waterfall. Somebody might have wandered in from Snowdin after you, but then they'd be talking to you, wouldn't they? Maybe they're from Hotland. It's not a human; you would know their spirit and style immediately. You lean over the rope and squint. The bridge shakes vibrantly under you but you keep balance well - you've practiced leaping from one bridge to the other before, anyways.
(It sends a thrill through you, defying death that closely-)
It's a lizardwoman; short, round, in a labcoat. That's definitely not Waterfall wear. You think you've seen her before, on your visits to the castle? Maybe. She's familiar, but not familiar enough to call forth a name.
Whoever she is, she's preoccupied, and after a minute or two of standing still and watching you realize she's not going anywhere, so you sneak in closer; you know how to be stealthy with or without your armour. It's only the work of a few seconds to scramble down the cliffside and then perch at the edge of the rope bridge. You stick to the shadows, just in case.
She's not even paying any attention to her surroundings, you realize; you probably could have clomped your way down here in full plate and she wouldn't have noticed. She's not looking left or right, just down, where the water and mist and trash all disappear to… somewhere.
(You're not sure where; you've thrown spears down there and they just disappear without ever striking anything.)
She's holding onto the bridge railings like a lifeline. Her hands are too tight, then too loose; gripping the splintering rope and then twisting it with fidgeting anxiousness. Somehow, it sends a chill down your spine that rivals anything the waterfall's thrown at you. Something about this is too desperate, too - something. You don't like that look. You should say something.
But you tend to scare people wherever you go, and you've learned that, so as much as you'd love to follow your instinct and just grab and toss her back up the cliffside, you make some noise instead; you let your feet shuffle, you run your hands along the rope; you wring your hair and manage to get it at least partially drained, even though the mist will probably have it soaked through again before you leave here.
By the time you lean down on the rope bridge next to her, she's coughing and polishing her glasses, a light red tinge coalescing in her cheeks. It's kind of endearing. She's small, you realize, for all her roundness; you're leaning down on the rope, almost bent at the waist, and she's pulling it down with all her weight just to get her chin on it.
"Hey," you greet, "I've seen you before. You're the Royal Scientist, right?"
It's not the smoothest as far as opening lines go - why are you thinking about that? - but it serves the purpose; she nods, adjusting her glasses, and her blush renews. "Ah - y-yes! Yes, that's me!"
She's skittish, and you don't know what else to do, so you do what you do best - flash the biggest grin you can manage, the one that shows all of your teeth. "Good! That means you're smart. You can answer questions. Right?"
"W-what kind of questions?" Against her better judgement, probably, she's answering you, she's interested. Good, you think, and it is, although you're not sure why. It's just a gut instinct. Keep her talking. Well, you do actually have a question you can think of.
"Every time I come here, I always wonder where it goes," you say, and you lean over the rope - sure of your balance and wanting to get a closer look. You can't see any more than you did before; the water and mist just drifts out into endless blackness. "The garbage comes from the surface, every monster knows that. But nobody seems to know where it goes. Do you know?"
"Ah," she says again, which is how most of her sentences seem to begin. She fidgets, but then something seems to click behind her eyes; she removes a hand from the railing to gesture, turning towards you. "Well! A-actually, I've developed quite a few theories! The standing one is that the physical matter dissolves and magic returns to the underground as a whole - "
She goes on for awhile. It was an idle question, but it's actually fascinating to listen; her explanations are thorough, and when you spontaneously interrupt her once or twice with questions, she doesn't get mad or impatient; she stumbles a bit but then answers with increasing surety. She takes her other hand away from the bridge to polish her glasses; the claws on her feet nervously nudge each other. She's not nervous of you, you eventually realize: she's nervous of everything. But her voice grows stronger the longer she speaks, and the tremors and stutters have disappeared almost entirely by the time she's started running out of things to say.
Then she realizes she's run out of things to say and turns red again.
"Well," you interrupt fiercely before she can get caught up in the whatever-it-was again. "That was ...actually pretty neat! Normally I just come here to look for junk in the waterfall. There's a lot of good stuff here. Nobody else really ever hangs out at this one. It has the best stuff!"
"Really," she replies, and then you see that something clicking behind her eyes again, like a puzzle piece being set down firmly. "Th-that's good to know! Not, uh, not that I'd want to take stuff away from you, I mean -"
You grin again. "You won't. Unless you want swords. Then you can't have them! They're mine. I need them for the Royal Guard." Or, you know, for yourself. Most of the time. Sometimes Doggo wants a new knife. Lesser Dog should probably get a better sword, come to think of it...
"No swords," the lizardwoman promises. Then her eyebrows raise above the rim of her glasses. "Oh! Oh, are you… Undyne?"
"That's me!" you affirm. She's heard of you! Good. Everyone should know about you.
"Oh!" She turns red again. Boy, she does that easy. "I'm, uh, Alphys! The - the Royal Scientist!"
You don't bother pointing out that you knew that already. Well, half of that. "Right! I knew I'd seen you before somewhere. That's why you're so smart!"
At some point you'd sat down, dangling your feet from the bridge; you use the rope to right yourself in a single smooth motion. "It's getting late. You probably need to get back to doing Important Science Things, right? But you're free to check out the waterfall whenever you want."
She looks surprised, and then nods automatically, seeming dazed. "Right! U-uh, I should - I should go. Yeah! See you around?"
"Of course," you reply, with one more teeth-flashing grin. The smile you get in return is tentative, and then she's lumbering away, little body rocking back and forth across the bridge.
You always trust your gut, and as you turn in the opposite direction, it's telling you that something about this was a very good thing. You head home with droplets in your hair and a bounce in your step.