Woman: "Of course!"
She collects the smaller cores, then heads to a clerk manning one of several windows set in the wall of the guild to retrieve your payment. A bit of talking later, and she returns with your 145 Drachmas (Dr).
Woman: "If you don't mind me asking, what do you think you'll do with the core?"

Hm, that's a good question. Probably too small to be turned into armor, but it could be the core component for a magic weapon, or turned into some accessories even. Hell, it's a pretty big core, maybe even more than one thing.

Woman: "Oh my, the entire core on one staff? Well, you will certainly have an effective healer then!"
Karina: "Safety is the top priority!"
Frederic: "Agreed."
Woman: "Well if that's what you're going for, I can recommend a craftsman for you. He's quite popular among new adventurers, his creations tend to be easy to use without sacrificing strength. The craftsman's name is Boreg, and he owns a shop called Fresh Rain Craftworks. I'll write down the address for you."
She takes another small sheet of paper and scribbles down some directions, then hands it over to you with a smile. Hm, not too far away.

You thank the woman, and head out to the streets to find this craftworks. The directions guide you into a crafting district, with many smiths, smelters, forges, artisans, carpenters, and craftsmen of every variety live. Most are tailored towards Adventurers and outfitting them, but there are still some more ordinary shops around. You find Fresh Rain pretty quickly; a tall, medium sized building with a large open air area filled with all sorts of equipment, the main building adorned with a large blue water droplet logo. Several young but muscular men are working on various things. A few leather pieces that will probably become armor, one fiddling with a long rifle, two cooperating to move a large ivory tusk over to a large stone workbench.
Most notable among the workers is an older man hammering a red hot sword at an anvil. By the look of his arms, he's been swinging a hammer for years; leathery and hard, and built of iron hard muscles. You assume this man is Boreg.

As you approach, he glances over while continuing to hammer the sword without looking.
Boreg?: "Yes?"

Boreg: "Aye. Hm. Water based."
He turns his gaze back to the sword and continues hammering for a bit. You're almost about to say something, when he speaks first.
Boreg: "Big fish? Or, frog. Big frog."
He nods to himself as he continues hammering, then dunks the sword into a nearby bin of water and looks back to your group.

Boreg pauses, then looks back towards you.
Boreg: "A slime?
... Oi, Largo."
Largo?: "Yes, Boreg?"
Boreg: "Take over."
One of the younger workers hustles over, taking the tongs and sword from Boreg as he stands up. The grizzled craftsman walks towards you and extends his hand, and you hand over the slime core. He then takes a few moments to examine the core, tapping it, looking close at its surface and checking it in the sun, running his fingers over it. After a few minutes, he's apparently satisfied and looks back to the three of you, raising an eyebrow.
Boreg: "Well, damn. A slime. Not bad, kids. What do you want with it?"

Boreg: "All of it? That'd be daft. You sure?"
Frederic tenses a bit.
Frederic: "And why would that be."
Boreg: "Oi. Girly. You the healer? You know much about your spells? How much does that staff improve yer healing."
Karina: "Eh? Um, well... Not, much I suppose? It helps more for my other spells, but, my healing magic is... Barely... Affected. Oh."
Boreg: "Aye. Healers don't get much out of raw power. Special gear, or lots of power. This core won't give lots of power, and a staff won't have special effects. If ye had an attackin' or support mage, they could use a good staff.
Ye want my recommendations?"

Boreg: "What do ye do then? The other two I can guess, I see your guns, but anything else?"