Singe can be found in the Earth realm, in the section just before finding the mysterious tower that leads into the Labyrinth, a key point in the game's story.
How do you fight singe?
You want to roll away and keep rolling if you're ever not behind cover. Head to either the left or right side of the room and use the ruined buildings for cover, though Singe will usually give you a break before he starts his fire attacks again. Try to get close enough to do maximum damage with your weapons.
Is Singe the Dragon remnant?
Although Singe is a dragon, we don't have to worry about firing into the air - the boss rarely leaves the ground. Nevertheless, the fight against him isn't easy, especially since it is one of the initial bosses.