Shyvana top lane is quite strong. I don't jungle with her often, opting for other junglers with hard crowd control. This is a simple build I've been using for a while now. I often change things around, but I've liked this build thus far. Skill sequence may be a bit off.

Greater Mark of Desolation
Makes her hurt.

Greater Seal of Armor
Early defense is nice.

Greater Glyph of Scaling Magic Resist
More durability, especially considering you've got solo top lane.

Greater Quintessence of Desolation
Makes her hurt some more.

I use Teleport and Flash, so Summoner's Insight is necessary. Buff duration, tankiness, and attack speed. I truthfully enjoy all three trees, and I have tried them, so I ended up trying to take what I can from all three.

Boots and Health Potion's are my favorite items to start with her because I always solo her in top lane. I find that it allows her to have an easier way to get around for last hits and possible harassment.

Vampiric Scepter is the next item I get for lane sustain before I get Wriggle's Lantern. I know a lot of people don't like getting this time unless in certain situations, but I find it to be perfect for her for the extra damage, lane sustain, and free ward that I'll need in top lane.

Mercury's Treads are self-explanatory.

Wit's End is an item that I personally enjoy because it gives the attack speed that is needed for her unique mechanic, and I enjoy the extra magic resistance to stay on any nuking champions.

Phage
Health and a slow that I enjoy without red buff. Builds into Frozen Mallet.

Frozen Mallet
Built from Phage. Even more health and guaranteed slow.

Atma's Impaler is a given for any Attack Damage character that gets a lot of health.

Warmog's Armor is good for the extra health for survivability and for Atma's Impaler.

Aside from Dragon's Descent, I find that Shyvana should max Burnout as soon as possible for chasing, escaping, and all sorts of usefulness. Twin Bite and Flame Breath can be maxed whenever after the other two. Twin Bite doesn't really scale that much with each level, but it is more useful than Flame Breath maxed in my opinion. Up to you.

Teleport
Map awareness and control. Incredible to initiate a Dragon Fight when there's a ward and it is a bottom lane fight. A quick teleport to get assists/kills to put you ahead. Plus, getting back to lane faster is incredible in keeping ahead.

Flash
Escape, chase, etc. Pretty necessary despite its short range compared to before. Along with Dragon's Descent, it can cross walls for many uses.

Jungling with her is fun, and pretty quick, but sometimes it's difficult to gank considering she doesn't have a hard CC. However, she's still viable for jungling. I just enjoy her in solo top lane much better. She can be beaten by other solo top champions, but she's very strong nonetheless and can become a terror should she get ahead.