I recently figured out this build after my friends told me to stack tank once as Shyvana and it worked out so well so I'm basically writing it down here.
Furthermore, this is my first time publishing a build, so feel free to stagger from this build for stuff if you want.

Well, this is a tanky build for Shyvana. It's a mix of tank and AD carry, really. By the end of this build, Shyv will have at least 3 slows on enemies, 2 kinds of flashes, and on top of all that, great defense and AD. She'll be great for team fights and chasing that enemy champion with all of 200 Health left.

I didn't put anything for runes because I never really used them and therefore don't know what would be the best. So... do whatever you want for those.

As for masteries, it's quite literally a tank/ AD stack. Not much to say.

One thing to say here: Get Twin Bite up the fastest because it's awesome like that. But, since you won't get boots for a while, make sure to start with Burnout and add one or two levels to it before Twin Bite is up all the way if you want. Flame Breath is really only good for that last hit if Flash is on cooldown or for poking enemies. Not much else. It is good for farming if you're in Dragon Form, though.

Start with a Doran's Shield, then start building for a Randuin's Omen. Sell the Shield and get boots, then Berserker's Greaves. Then, a Giant's belt and Phage, to build Frozen Mallet. This makes chasing enemies all the much easier now, because you have Exhaust, this, and Randuin's Omen. After this, it's stacking AD. Get a B.F. Sword, then a Black Cleaver. Get a Stinger or something to get that Attack Speed up, and then finally another B.F. Sword and soon enough, Infinity Edge. Boom.

You may want to get the red buff semi-early on in the game, before you have frozen mallet. With Randuin's, you'll be all set to solo it, even if you're level 5 or something. Maybe have an ally help you if you don't think you'll be able to solo that early on.

When/if your team gets Baron, you should be the one to initiate because of your defense, and you can protect your allies while they kick that snake...thing's tail.

Use Burnout to farm quicker and if your in Dragon form, all your abilities are useful for farming. Just take care to not Dragon too much, as you can use it as an extra flash if you need to. I generally don't Dragon to farm, but I'll farm as dragon if I'm already in the form.

With you being the tank, having 3 different slows, 2 flashes, and rally good defense and AD, you're the best to initiate a gank or a fight in general.