This is a boss fight on the way to the True Ending path of the game. Spoiler details below:
*** Spoiler - click to reveal ***In order to fight Romeo (this is on the True Ending path), you must "Rebel" against his command when you speak to him after defeating all 5 Messengers and Nameless (in Nowhere via the Arcane Portal).
The fight starts off against the Red Lady, who isn't much of a challenge, and can be taken down without too much hassle. It is advised to try and get through this part of the fight without using any decent items, as Romeo can be a tough bastard.
As for the Romeo stage of the fight, I found it easier to keep my distance and attack with magic during the earlier phases - but once he starts picking up speed and aggressiveness (particularly when he drastically increases the frequency of his nasty ground-sword attack), I switched to melee attacks and weaved around him with Assault+dodges, while buffing myself with some attack/defense items.
Keep an eye out for the Red Lady - she appears again during the fight and can start healing Romeo. Take her out ASAP with long-range magic, so that you can continue to work on getting his health down using the assault+dodge tactic
I personally found this boss to be those most challenging of all the non-secret bosses - so don't feel discouraged if it takes you a number of attempts.