You will first be really passive exept if you can couter gank well you will just farm until lvl 6 you will also do drake early lvl 4 you can solo it.

Once you get your core you will try to gank every time you can and even force the gank with ghost.

You will be strong with you first item so dont worry and try to fight a lot cause you do massive dammage if you do your combo well R>Z>A>Q>HYDRA>E>A your rune proke instantly so you will do massive damage and even 1 burst 0 life or defense item ennemy just remember to proke your rune before breath, if you are runnin always use your breath to kite back as it slow the ennemy.

Its the safest road in the early jungle and its help securing dragon scuttle.

You start red buff if its bot side you then go to blue buff and do your top side jgl kill the wolf last then recal grab boots and head to the crow you smite the big one do scuttle then, gank with ghost (mid or bot), or golem recall grab blue smite pink ward head drake. Red buff top full clear red(for golem run around big golem to escape litle golem damage smite crow then back grab boots go blue buff then scutlle. If you can gank either mid or bot try to get a flash or even a kill then finish jungle recall...

Welp there it is end of what i have to say about shyvana HP Carry.
I will soon create a AP Shyvana guide for those that want to check it both are strong but the playstyle and item are comlpletly different and i personnaly think that this build is better overall if you manage to secure objective.
Hope it will help some to love that dragon wich i love so much^^!