Botrk and Black Cleaver

to magic damage focused. BC is just not a good item on her, since she can only apply it with AAs (most people who use BC well have AoE or DoT physical damage in their kits, like Garen, Wukong, Hecarim, and Urgot. Almost all of Shyvana's damage is magical, meaning she has no need for and no way to easily apply the armor shred.

Cleaver's not a good pick for Shyvana, and while BotRK is strong, she actually does better with Wit's End.

Shyvanna's only sources of physical damage are auto attacks and Q, which is an auto attack modifier. You won't get a whole lot of value out of Black Cleaver.

However, the Phage passive can be useful for her.

Bortk is pretty good on Shyvanna as well.

4 defensive items is really bad with two offensive items because you have no boots, and will get kited like crazy. Replace one of your defensive items with boots and you should be good.