The Fire Beasts are small, animal-like ghosts that spread fire all around them. These critters, along with three much more sinister ghosts, started a fire in a Woody House. They usually appeared out of fire. Some of them were blue-colored and unable to be defeated or captured in any way. All of them vanished when other, more powerful ghosts were defeated and the fire stopped.
These critters usually appear in groups. The red ones can be defeated rather easily but the blue ones can only be defeated by their love of fire. If you encounter a little blue flame on the ground: I know it's tempting, but don't poke it, step on it, shoot it, or bother it in any way. It'll turn into one of these guys and bring little red buddies with it.
To evade a blue Fire Beast you can jump over it while it's still a little flame, crawl under it when it jumps, or run like a chicken to the nearest fiery pit and leap for your life - it'll dive into the flames without a backward glance.
Red Fire Beasts are easily evaded and vanquished so long as they don't have blue backup. If you encounter a wall of flames, particularly one that shrinks and swells, you may find that red Fire Beasts leap out of it. For that reason, shoot the fire wall until you get a chance to jump over it.