The Quetzal Quatl temple consists of stages 4-6. The levels are repeated from the first temple (4-1 is the same as 1-1, 4-2 is the same as 1-2, and so on), but more points are required to pass and a new purple ball is added to the mix. In addition there is an additional sixth level at the end of each stage. In all there are 18 levels in this temple. After level 6-6 there is an amusing cutscene during which the achievement unlocks.
You can start a new adventure game at the beginning of any stage you have reached, but I recommend starting at the beginning to build up a reserve of extra lives and to get more practice.