I understand that shyvana's core items have all been nerfed. I believe they were Frozen Mallet, Wit's End, and Atma's Impaler. Either its been through cost or a lowering of stats. I'm assuming people are playing a tanky Shyvana.
I've been playing Shyvana since Season 2 when she came out, but only recently started playing her again since seeing these threads. A good idea I picked up from another thread was that with the Season 3 Item overhaul, we need to change how we build Shyvana.
To be able to do this, we have to understand her basic kit. These are generalizations.
Passive: Some Attack Speed is essential. And in Dragon form, all abilities become AoE.
Q. Twin Bite: Scales with AD and on hit effects
W. Burnout: Scales with AD, but does MAGIC DAMAGE
E. Flame Breath: Scales with AP
R: Dragon's Descent: Scales with AP
What can we determine from this? Shyvana is a hybrid, an abnormal Hybrid at that. It also means that she has a very flexible build. While I do say she is a Hybrid, I don't suggest you focus on building AP, Shyvana is like Jax in the way that a little AP goes a long way. That also means magic penetration will maximize your damage output. Having said all that, what possible item gives AP, AS and MR shred?
The answer is Malady.
+25 ability power
+45% attack speed
Unique: Your basic attacks deal 15 + 10% AP bonus magic damage.
Unique: Your basic attacks reduce enemy magic resistance by 4 for 8 seconds (maximum 7 stacks)
This will replace Wit's End as a core item. Since most builds go R<W<Q<E, that means W. Burnout is ranked first, it does AoE MAGIC DAMAGE. Each second an enemy is close enough for you to autoattack them, the worse Burnout is going to hurt. And when it comes to teamfights, every time you Q in dragon form, everyone is going to lose their MR.
Frozen Mallet (or Trinity if you prefer) is essential to keep targets close.
Whether toplane or jungling, an early Wriggles lantern will help with sustain, which can be later sold for Ravenous Hydra. After Malady and Frozen Mallet, the build choice depends on the game.
Good items on Shyvana:
AS: Malady, Trinity Force, Zephyr, Wit's End, Nashor's Tooth, Statikk Shiv.
AD: Frozen Mallet, Black Cleaver, Blood Thirster, Youmoo's Ghostblade
Lifesteal: Ravenous Hydra, BoRK, Hextech Gunblade
MR: Runic Bulwark, Maw of Mallortius, Mercurial Scimitar, Spirit Visage
AR: Sunfire Cape, Randuin's Omen, Spirit of the Ancient Golem
CDR: Nashor's Tooth, Zephyr, Black Cleaver, Ionian Boots of Lucidity
This is a build I put together for a Tank Shyvana. It gives enough survivability and damage to be able to peel.
Merc Treads, Frozen Mallet, Malady, Randuin's Omen, Maw of M., Ravenous Hydra
Soviet Swain Approves Shyvana Builds
TLDR: Try building Malady early, it will help with your damage output since 3/4th of your abilities deal magic damage. Just try it out for one match, then look at the stats and see if you deal more Magic Damage or Attack Damage at the end of the game.
P.S. I was surprised, the stats told me 2/3s of my total damage was magic as Shyvana.