Eliminate these and then bring 10 horns back here with you. To me...
The Rememberer

Make sure to report to The Rememberer of the result after eliminating the monsters!

...

Ahh, concentrate! Phew... the art of levitation is such a delicate one that requires so much energy and effort, that one mishap can surely ruin it all. Please talk to me in whispers next time!

Anyway how can I help you?... Oh! You! Did you find the Jr. Boogies by chance? Ever since they transformed into a hideous creature thanks to pollution, they have been notorious for attacking travelers from left and right. I know it's only 10, but I think that buys some time for travelers to walk around safely for a few. Were their horns contaminated, too? I knew it. For you to last its attack looking unscathed... wow...

I can tell you're noble enough to do this without expecting anything return, but this is just my way of saying thank you for helping us out. Please take it.

You're not saying that you're going to end your journey here, right? Inside the Dungeon, you'll find nothing but really powerful, dangerous monsters. I've put up bulletin boards everywhere, so find those. I'll reward you well, if the job is done right. Watch out for those monsters!