Well, these two are linked, so that's not a huge surprise.
Here's a hint. You need to get slimed by the green slime dragons in the cave... then remove the slime using a nearby heat source... and then take the item you get to a certain person... and finally, interact with that item when it's sitting out on display.
I don't want to completely spell it out for you, so I trust you'll be able to figure it out from this. Good luck.