Dingodile is the second boss in the Third game. Again, you must survive three rounds, each slightly more difficult than the last.
At the start of each round, Dingodile will shoot fireballs in a circle around the arena. Avoid them. Then, he'll start firing flamethrower blasts, destroying his barrier. If he destroys his barriers completely, he'll resummon them and start over. Instead, once the barriers are sufficiently destroyed, run in and spin him. Then, you'll need to escape before he explodes. Watch that enough of the barrier is destroyed that you can get in and out quickly.
Repeat three times to unlock the achievement and double jumping.