Shyvana is great in the new jungle, champions with AOE spells, I personally find the best now. She can make really healthy clears, and gank often because of this. The new Jungle also offers more exp, so we reach lvl 6 faster.

I build Shyvana like this for early gank power. I often gank at lvl 4 when I have my Stalker's Blade so as to help my team.
BUT
You can, and most do, build her with pure movementspeed quints like this-Most build her this way because has no ability to keep close to the enemy champ, or gap closer, apart from the ult.

There are lots of jungle items for shyvana, but personally I find Stalker's Blade with the Enchantment: Devourer to be best for Shyvana. The reason for this, is because I use blue smite as a means to catch-up with the enemy champ as blue smite slows.
The reason for the devourer is because it scales awesome with Shyvana.

Dashbie why not Enchantment: Cinderhulk? I don't wanna use this, because it means we can't use Sunfire Aegis, as these two items has the same passive, called "immolate" but cinderhulk has a weaker version of this.

The late game damage item, is not there are four primary damage items for Shyvana- Hydra, Cleaver and Steraks gage. You see what to build as you wtach the enemyteam develop.
If the enemy carry is strong, Hydra is for you, you are tanky and a great back line diver with ulti. Is it more the top laner that's fed get cleaver, and negate some their armor stats for your own adc.