I'm not saying my build is the best or anything like that, I just noticed that, so far, it has never ever failed for me.
Here are my last games played with Shyvana, so you can see that without being out of the extraordinary, stats are still good.

Pros

Good melee
Nice damages
Fast pusher
Manage easily a 1 vs 1

Cons

No slow or stuns
If focused early game, can be taken down easily
No real range spell

Why this build?

Simply because it works just fine, let me details that:

Shyvana has good damages and is an incredible good melee character, hence I go for lifesteal, health and armor early game so that i can farm real fast and get a kill or two if possible.

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As I begin playing on a lane, I go for the Doran's shield, for the health and armor.
Since Shyvana has good farming skills, you can easily earn money to buy the Boots of Speedand, if you haven't met any troubles, you can even go for a Vampiric Scepter.

The reason I choose Wriggle's lanternat first is because of the armor and lifesteal (Ward is nice too :p). As you get this item you can rush in and try to have a kill (and that usually happens).

The boots:
I usually go for Mercury tread'sbut when I encounter a team composed of at least 4 ad i tend to go for the Ninja's tabi.

Next is Trinity; i just love this item whenever i play an ad off tank as it does really good damages and a nice start up! With crits runes, you do considerable damages and crits and taking down ennemies in melee will be easy .

As you noticed, i go for the Atma's Impalerbuild so I buy a Frozen Mallet( let's consider the fact that Shyvana doesn't have any stun or slow, meaning the Frozen Malletis a must have to finish off enemies with your w / Get that item after Trinity).

Last item is either Warmog's armoror Black clever; i choosed to put Black clever as you'll find enemies with armor and you'll appreciate the armor pen(here again that depends on the team you'll encounter).

EVER LASTING GAME:

I happened to have lasting games and good opponents. I decided to sold my boots for Phantom dancerto end the game faster.

If a lot of AP in the other team (3+):
You can go for the Wit's Endinstead of the Atma's.

My runes are the same for all my ad characters, I always have a 22% crit when beginning a game, and I just like it this way.

If you don't feel like taking thoses runes I'd go for tanky runes, I really think when it comes to damages Shyvana has what it takes to take down any enemy (I managed to take down in a 1vs1 solo, no lvl difference a Gangplank, an Irelia, Fiddle, a Lee Sin and even an Udyr; only Xin has been dangerous so far).

I chosed Ignite and Flash and never felt like changing those (for the moment, let's see how flash is gonna be nerfed).

Ignite is the summoner spell that helps me take down an ennemy with lifesteal in a 1vs1 (Irelia, Lee Sin, Fiddlestick, Vladimir etc...).
I also use it when in melee I happen to notice a character who's about to get away with Flash or Ghost.

Flash, on the other hand is my last moment flee spell while using my Q and my "Finish Him" spell as well.

A piece of advice:

Try to farm as much as possible early, that will give you a huge advantage and don't hesitate to harass the ennemies on your lane with your buddy as this build will deal good damages early game.

When soloing, just farm, don't try to get a kill except if you already have the lantern and boots in a 1vs1. You should have already placed you ward to see if the ennemy jungler is comming and you can make many soloing character go back, if not killing them, be confident and don't forget you have a lifesteal !!!(sometimes backing because you feel you'll loose the fight is what makes you miss the kill or worst, what makes you die)