Shyvana is a very strong champion that can deal tons of magical and physical damages at the same time. I really play as a damage dealer with a good resistance and armor given by atma and wit's end for the end. My build is based on her Q and W skills. They are only based on damages.
So I play her full damages and attack speed to deal physical AND magical damages at the same time.

My seals of defense are taken to deal at the begining with her low defense that could be bad when you want to play aggressive from the beginning.
The armor penetration is to deal more damages when i got the BF and alacrity for my speed attack that is a little low on the beginning. Shyvana needs some cooldowns for her abilities which explains my glyphs.
At the end she really needs to be fester than the opponent so i take some movement speed.

My masteries are here to help me do my abilities as often as i want and to have magic reduction for the W skill.

I begin with the vampiric sceptre that could seem a little low but it helps me hold a lane longer than others and adding 10 of damages at the beginning doesnt help you a lot at the beginning. After that I really try to take the boots as fast as I can and after that i focus on damages and speed attack. At the end of the game I take warmog/atma for the survability and the damages it adds me.

I hoped you liked my build. It really does tons of damages at the end of the game though it's a little low if you haven't been able to feed a little at the beginning of the game.