AP Shyvana?
How? That sounds interesting but the only thing I can think of that scales is her E?
She's an odd beast. 2 of her abilities scale with AD, 2 with AP. But 3 of her abilities are magic damage (her W most notably). So it's very advantageous to lower people's magic resistances. Especially if you're buying the attack speed/magic on hit items like Ionic Spark/Wit's End/Mandreds.