Fluffy will start the fight by either jumping from the second floor to the other side or with a glowing light in his hand that will cause a bunch of pillars of light to come up and attack. When this happens wait a second and stay off the yellowish color that will be in your area.
He may do this a couple times or he will jump and slam to the ground, this hurts anything in the immediate area. From there he might slam his fist to the ground. This causes the light pillars to start.
While on the ground, he may move his left arm forward and his body back, as if ready to leap forward. This signals his half-rotation sweep attack, where he leaps forward while spinning counter-clockwise and faces the stairs for about 6 seconds; he rotates clockwise afterward and resets his position. It is a good idea to stay to the right side of the stairs, as his tail allows him a great range of arc on the left side, due to his pivotal point being his left arm. He will rotate clockwise to reset his position, again sweeping his tail on the left side.
One of his strongest attacks is a frontal laser breath attack which goes in a straight line towards where he was facing.