Since Shyvana is free this week I decided to play her as a jungler. All is well but I am having trouble with picking my jungling item. Some people say that Wriggle's Lantern is horrible and the Golem is the way to go, while others say the opposite. Can anyone set this straight? Thank you!
I play shyvana alot, and often in the jungle. I play her as an off tank, with high clear speed, and move speed, so that I can gank often and split push WHILE farming the jungle. And after thourough testing have decided that Spirit Stone is the best jungle item. Great damage for 700 gold, amazing health sustain from the 6% life gain, ON BURNOUT. Burnout does immense damage in an aoe, and the Elder Lizard is NOT a reduced heal for aoe skills.
I rush spirit stone, then go Ravenous Hydra. This gives you INSANE clear speeds, and high damage for those early ganks. Then I finish the elder Lizard. These two together let you walk up to a camp, E, Q, Active on Hydra, move on to next camp. If you are good at stringing AA resets. Fast clears = more ganks, more ganks gives lots of map pressure. Also super high healing rate in the jungle, cause the elder lizard heals stacks with the Hydra's splash.
General Jungling build thoughts. Less on topic, skip if you want.
Just those two combined gets you over 105 ad (without your own stats), at 5.3k Gold. After that build what fits the situation.
Item: When I prioritize it.
Triforce: Getting away with ganking often/enemy team dealing low damage. Better early
Spirit Visage: Enemy team deals magic damage. I choose this over Banshees because the CD is good on shyvana. Synergy with the hydra/Lizard combo is great
Randuins: With this, shyvana's stats/passive. you get to 170 armor. Enough to feel tough against other bruisers, not enough to tank out a carry.
Sunfire Cape: Bonus to overall damage output but less defense than randuins. Choose if you are avoiding damage, but dealing it out.
Thornmail: 2 or more AA based champs in the game. GET THIS FAST.
Frozen Mallet: Enemies running away/kiting alot, this will make you stay relevent against slippery targets.
Black Cleaver: AA, twin Bite, Hydra active, 4 stacks in under a second. CD/ HP great on Shyvana. Highly recommended.
Atmas: a great 6th slot item. after other items giving HP, make that hp mean more
Boots: You make the choice, every game it should be a choice based off of what is happening.
My prefered build: In order I common get them. Hydra, Lizard, Boots, Spirit Visage, Sunfire, Atmas
On Runes and masteries use your preferances,
I run Shyvana with 19 flat ad runes, and scaling CD quints 15%. That is all, the ad makes burnout hit harder. Dead things do less damage. I love CD
Masteries are 9\21\0 on my build.
and 
or 
is what you should have now
6th is your variable slot depending on what your team needs.
Zephyr can be ok if you didnt get merc treads but super late game homeguards can be worth keeping
is a solid pick vs AOE AP heavy teams and helps your team stay alive more in teamfights
can be considered if vision is a problem and adds to your tankiness
vs very AA dependent team comps and if more armor is needed
If you kept 
you can choose to have it especially if there's decent stacks on it. If your team needs a stronger front line you can swap it out for 
for more armor and massive HP bonus with +25% health along with your other tank items
solid too
