I typically go with Feral Flare, boots 1, BOTRK then finish boots. Then I'm kinda lost. My last game I was against a Jayce, Zilean Mid, Nami, Ezreal and Rengar. I had as items Feral Flare (sold it for warmogs), merc treads, thornmail, botrk, Hydra, spirit visage and warmogs.
I didnt feel like i contributed much even though we won.
I was 7/8/17, with 31.4k damage to champions, took 55.8k damage, and the game lasted 53 minutes.
Flare -> Boots -> BotRK -> tanky. If they have a lot of physical damage, Randuin's gives armor, health, and a CC active. Sunfire is a slightly damagier version without the CC. Thornmail is OK if the enemy team has a really fed ADC and you have a health-giving item or two. I wouldn't build a Frozen Heart on Shyvana since the mana would go to waste. If they have a lot of magic damage, Spirit Visage gives MR, CDR, HP, and increases the amount of life steal you get from your life steal items. Banshee's Veil is better if they have game-changing abilities you need to dodge (Morg binding, Thresh hook, Nid spears etc). Locket of the Iron Solari is good if you need AoE magic resist (Katarina, Akali...) and it gives some CDR and a nice shield active. For health, you can get it by building any of the MR items mentioned, a Randuin's or a Sunfire. For health-specific items, there's Warmog's Armor, Frozen Mallet and Ruby Sightstone. (A Sightstone is a nice addition to your team's vision. Wards save lives!)
With the new changes to jungle items coming soon in season 5, Shyvana shouldn't need to change much in her build path. Just keep doing FF into boots 1 and hydra/botrk, then finish boots and start building tanky. With the new changes to how jungle items change smite coming out, she will be alot harder to deal with as she is.
Flare -> Mercs -> Sunfire -> Wit's End / Randuin's / Banshee's
Pick your 4th item based on who is fed. If no one's fed Wit's End is a good damage item. BotRK is a noobtrap; Wit's End will increase your damage by a lot more.
ill give this a shot, but not having any life-steal seems really bad :o
I tried it out. It went pretty good. Though I really do miss the life-steal and the active from botrk. Wits end had good use against a team with a katarina and a udyr. I did fairly well.
