Sky Blade Sword of the Heavens (2004)

Blurb:
Two are destined to be conquerors... but only one can succeed! Jih-Ro was destined from birth to become a great conqueror. But then he learns that there is another-someone born on the same day at the same time-who shares this destiny. One must become the conqueror-the other must die! While searching for the other destined one, Jih-Ro meets Il-Geum. When he learns that Il-Geum was born on the same day at the same time, he begins to suspect that Il-Geum is the other one. Their meeting proves to be no mere coincidence, however, as they continue on a journey filed with danger, humor, and the promise of new friendships.

Source: www.anisearch.com/manga/243