I clicked on your mint dragon egg. You get rare dragons the same as any other except four specific dragons. Three of those are obtained by breeding two other dragons. Like a Bluna is a crossbread of a Water and a Skywing, Shallow water= Water + Magi, Geode Green + Stone. Also, the fourth is Gaurdian of Nature which is obtained by getting three other rae drags, but not breeding. Besides those four, all of them are found the same way you got yours.