Alright, here we go:
Sebastian, bored from all his soul sucking tom foolery, takes a much needed vacation to Japan, where he meets, you guessed it, Neuro! He decides he wants to screw with someone, enter Katsuragi Yako, minding her own business at the local convenience store, right? So Sebastian, being the royal jackass that he is, ninjas his way into the aisle behind her, pretending to look over a box of pocky, all the while he's mentally harassing poor Yako.
Enter Sata..I mean, Neuro. You see, Neuro is the kind of guy that takes pride in his work, so he sees Sebastian and thinks to himself "Oh hell no, we can't have this shit!", so he strides into the store, grabs Sebastian by the head, as Neuro loves to do, and promptly throws him into a mailbox.
Sebastian, yeah, he doesn't like being tossed around so much, who could've guessed? Pissed, Sebastian busts out some knives and nails Neuro in the face: does he really expect this to work? So, Neuro's lying there all limp with that retarded smile on his face, his eyes glowing nuclear green like he just got back from Chernobyl, and then he sits up, laughs...and jumps to his feet.
With a flick of his wrist, Neuro has dropped something onto Sebastian's head, little does Sebastian know it's the Evil Violin, which Neuro intends on playing..with his Chainsaw arm!
The two demons decide to duke it out Super Smash Bros. style in the middle of a crowded city because, you know, that's totally what fashionable demons do. By the end of the conflict there are banana peels, cardboard boxes, and Kirby hats all over the place.