Tetrawings are descendants of the Hexastalker
. As forests developed, some hexastalkers turned to climb them to catch prey (either in pursuit of pinwheel bugs and to leap on larger vertibritoid prey). Some took to leaping from tree to tree. Some developed skin membranes to allow them to better glide, powerful central legs for leaping and eventually refined these features into a set of four wings: two in front serving as canards and two in the back that were the main lifting surface. These creatures were still amphibious and gave birth to dry.
As the world they evolved on had 0.9 g gravity the demands of flight were easier on earth. This allowed for a fairly rapid evolution of these creatures. In truth they were pretty clumbsy fliers (at least at first) but without competition the skies were theirs.