How to breed these types of dragon which have special elements (not fire, earth, plant etc.) on their tag in the game. They just have a sun, a moon or a rainbow. What basic elements should be mixed for each of them? Which kind of (hybrid I suppose) dragons should I mix to obtain those ones?
Rainbow Dragons are randomly bred from any combination that has at least 4 different elements.
Moon/Sun dragons can only be bred with a combo including cold and lightning. Sun dragons are bred between 7am and 7 pm while moon dragons are bred between 7pm and 7am. No, that's not a rumor. Dragons must be at least level 15 or higher or else this will be very difficult.
Scorch/Cold are popular pairings for both sun and moon.
Rainbow Dragons need at least 4 elements while Sun and Moon require Lightning and Cold. Sun Dragons can be bred between 7AM and 7PM on your device clock. Moon Dragons can be bred between 7PM and 7AM on your device clock. There are several possible combinations that can be used as listed on this handy chart.