When the lava T. rex has lost about three-quarters of his health, 4 fire shamans appear—one on each side of the room, standing on the round pillars in the lava. Each shaman has one of the red skulls, and each pillar has one of the 11 spider tiles you must activate to beat that particular reward challenge. The order in which you collect the skulls and activate the tiles doesn't matter. In the play-through shown below, we did the spider tiles first and came back later for the shamans and skulls, starting on the SW side of the room and moving clockwise.
As long as you've found all the other skulls and activated all 11 tiles, you'll receive 2 artifacts: a Serpent Drum Artifact (+ bomb, + speed) for the skulls and a White Drum Artifact (+ defense, + speed) for the tiles.