This guide is nowhere near complete but I figured I would get the build out there at least. I've been trying different jungle routes but I'm still not satisfied I'm also testing out AS marks as compared to ArP in the jungle because of her passive. For now I can describe my route and opening in the jungle but I don't have a lot of other points prepared and I'm still playing around with the build a lot and I'm sure many people will complain and find it unorthodox and weird but I'll talk more about that in the body of the guide.

So as any jungler knows there are a lot of different paths through the jungler depending on your champions strength and your or your teams strategy. I generally stick the the basic blue buff -> wolves -> wraiths -> golems -> blue pill -> red...
However Shyvana is not as strong as other junglers and will need a strong leash on blue in order to take it at level one. (I'm working with runes to see if this can be changed) otherwise Shyvana is a decent ganker leading in with the speed boost from Burnout and eventually chase with dragon's decent.

This next route is for when your jungling alone and don't want to rely on a leash. wolves -> wraiths -> golems -> blue pill buy boots -> blue -> red -> look for gank
Basically I start with Cloth Armor and 3 health pots. I then start with wolves and work my way over to double golems using potions in between camps. It's possible to do it with 2 pots but I take the third so if I mess up I don't look like a fool when I die. Once you blue pill pick up Boots and as many pots as I can carry 2 or 3 depending, if you got an early gank or kill pre-game or on your way through the jungle then you can pick up a vampiric sceptor and some pots but you need at least one pot. Then I go and get blue and red buffs and look for a gank.

The items differ slightly between the two builds but, the core is the same.

Core


These three items give a little bit of everything that we need. We get some AP, AD, HP and a lot of AS. The build focus mainly on AS and the mallet just rounds out durability nicely.

Offensive Items


These are the other three items i like to go for they are mainly offensive plus a little bit of MR. These will raise your AS significantly especially from Guisoo's Rageblade's stacks. These three also give you more of the hybrid damage that makes you less AD intensive.
your AD will only get up to about 170 or 190 depending on whether you jungled with Wriggles or not and whether you kept it. However, you get an additional 60 magic damage with Malady and Wit's End plus your AP will be around 100 so that you are able to deal some decent damage with Flame Breath and Dragon's Decent. Madred's Bloodrazor is also a viable option.

Other options (Situational)


These Items are mostly focused defensively except the gunblade. Guardians's Angel is a very good choice and I often go for it because it has both MR and AR plus a nice passive and Aegis of the Legion is the same way. Atma's is nice because it adds a little extra AD for you (about 62) plus it gives you armor if the other team is heavy AD. Hextech Gunblade is good because it plays more into your hybridness it will give you more AD and AP over AS if you decide that is what you prefer.