AP Shyvana is not very good and I don't claim it to be. Most other ways to build her are probably better. However AP Shyvana is fun to play in normal games when you want to try something new.

Shyvana scales off of AP on both her E and Ult. Her W scales off of AD, but deals Magic Damage, so Magic Pen will help that to do more damage even though it wont be your main damage tool. Her Q scales off of AD and deals Physical Damage, but it procs on hit effects, so it can be used for Lich Bane or Nashor's Tooth Procs. Generally AP Shyvana has sort of a poke syle when she's in her human form, but you can also play in people's faces and deal good damage as well. When she ults, she becomes incredibly bursty. Watch out when you ult though because this build makes you incredibly squishy, even with her passive.

This is my first guide and I realize it isn't very good. If anyone has some constructive criticism to give me, it would be greatly appreciated