Most players say AS - AD Shyvana is not playable. But they're wrong. You can play only AS - AD Shyvana because with high attack speed you gain so much rage in a short time so you can transform into dragon form more often. Shyvana's Dragon form is really powerful, so you need transform into the dragon form often. But AP Shyvana can't transform often as AS Shyvana. AS Shyvana more tanky, more dominant and more like a fighter. But AP Shyvana is really fragile like a mage champion. AS Shyvana can use her every skill but AP Shyvana can only use his E ability and this stuation makes her really boring champion. Okey AP Shyvana can kill everyone with her E skill but while his E skill is in cooldown you can't do anything against enemy.

If you want to have fun with Shyvana, you should play as AD - AS Shyvana. But if you want to one-shot to everyone you should play as AP. And don't forget, AP Shyvana is fragile so you should be careful in teamfights.