Wednesday search challenge (11/14/12): What kind of animal can do that?

There is a kind of animal that is remarkably adaptable.  To my amazement, I just found out that this animal--a vertebrate--comes in varieties that stretch the idea of what it means to be an animal with a backbone.  

There's one species of this kind of animal that somehow manages to live without lungs.  It doesn't have gills (as an adult) or some other pseudo-lung thing... just this amazing ability to absorb oxygen directly from the air without all of that unseemly huffing and puffing.  

Another species of this animal is also photosynthetic during a part of its life cycle.  Really?  A photosynthetic animal with a backbone?  (And I mean photosynthetic in an interesting way: that is, the animal actually gets part of its energy by photosynthesis, not that it has moss growing in its hair as a sloth might.)  

This week's question isn't terribly hard, but it's amazing: 

What Order of animal has both lungless and photosynthetic species within it?  

Note that I'm asking for the Order of the animal.  I mean this in the biological sense, following the usual taxonomy of Kingdom, Phylum, Class, Order, Genus, Species.  

And while it may not seem like it, the photo at the top is actually a clue to the answer.  

Think you know what it is?  Search it out and prove you know the order! 

Search on!