What enemy drops the Crystal Core? That's all I need for the first quest item.
Well, that and more slime concentrate.
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The Large Slime at the end of the Fae Forest. It's a rough fight if you're below level 5. Healing Potions aren't worth your time, they can't outheal the damage you take, and they're way too expensive to be worth purchasing. Sylphstone Gems are the way to go; they don't really state how much they heal, but I've found them to heal ~200 HP per use.
Bring plenty of artifacts, too. The Briarthorn necklace is very, very good for the fight, since all of the Large Slime's attacks are physical, and you can spend following turns healing with Sylphstone Gems (or leftover Healing Potions a gnome might've given you).