Dragon's Descent has a minimum duration of 16.66 seconds if no autoattacks are made. With an attackspeed of 1, the maximum duration is 25 seconds. With 1.5 it's 33.33 seconds. With an attack speed of 2.5, the maximum duration is 100 seconds, assuming that she is constantly attacking. These calculations do not take in account that Twin Bite doubles the amount of fury gained and can hit multiple targets in dragonform.
With good positioning and timing, Twin Bite can massively extend the duration of Dragon's Descent. By hitting three targets, it generates enough fury to stay in dragonform for another two seconds.
Twin Bite is a great turret pushing tool, as it allows you to autoattack 3 times in the time space of ~1.5. (taking into account attack animation time and casting time)
Shyvana's kit allow her to do large amount of damage over time at close-range, but it doesn't provide her with burst capabilities. Failure to combine Shyvana's abilities together to effectively constantly attack a target will create a weakness for a period of time that your opponents can take advantage of, so be aware of your enemies' potential methods to disengage from you.
Flame Breath may be a skillshot ability with a fairly long range, but a lot of its value is in its armor reduction and additional on-hit magic damage, so it is frequently better to cast it when you are close to the desired target.
While Flame Breath may not seem like an important skill to level up on an AD-focused Shyvana, keep in mind, that, between the armor reduction and additional on-hit effect, giving it a little priority during leveling can lead to surprisingly high damage output, especially, when deciding between leveling up Twin Bite or Flame Breath. The greater damage in a small amount of time of Flame Breath is also generally better for harassing in lane.
Both Trinity Force and Frozen Mallet are very powerful on Shyvana, but buying both is not recommended. Which one you upgrade your Phage into depends on the state of the current match, Trinity Force being the strategic upgrade you have to take your time with and Frozen Mallet being the tried and true early and mid-game choice.
Since, while in dragon form, 希瓦娜的Twin Bite ability affects all enemies in cone in-front of her, it triggers Tiamat's passive twice on every single enemy within range, causing the splash damage to scale exponentially rather than linearly.
Example: With 10 enemies in a cone in front of Shyvana, at rank 5, all enemies in a cone in front of her will take 200% of her auto-attack damage from Twin Bite. In addition, Tiamat's passive will splash half of that damage (100%) to each nearby enemy. This will be triggered 10 times (once for each enemy in range), but a target won't take their own splash damage, meaning they will be hit by 9 of the Tiamat splashes each. As such, every enemy in the cone will take 200% + (100%x9) = 1100% damage from 希瓦娜的Twin Bite attack.
Tiamat can also be stacked as it's effect is not unique, a video demonstrating this can be seen here
In Season Three, the passive of Tiamat is changed in Unique Passive, meaning that stacking Tiamat doesn't increase splash damage.
Heart of Gold provides extra gold which is especially helpful if Shyvana is jungling and thus has likely less potential gold-income compared to the laners. Later it can be upgraded to Randuin's Omen or sold after at least 13 minutes and 45 seconds.
Take note if Shyvana'sfury bar is full while you are attempting to kill her. The long range of Dragon's Descent can easily allow her to go over walls even while a fair distance away from them, so avoid wasting abilities with significant cooldowns and costs on her.
Dragon's Descent is not limited by cooldown - quickly gaining fury allows her ultimate to be ready long before yours if you misuse it.
Dragon's Descent requires fury, which is quickly gained by Shyvana autoattacking. That's a great opportunity to harass her from range and delay her ultimate.
Shyvana shines in an extended close-combat fight over time. Use champions with many options to disengage and do your best to avoid such a fight against her.
Shyvana has no natural ways to keep you in place for her to autoattack you. After using Dragon's Descent, she has little ability to catch up if crowd-controlled out of melee-range. Using crowd-control effects to hinder her movement during Burnout can also stop her from getting the ability to its maximum duration.
Burnout provides a very large amount of bonus movement speed at the beginning of the ability, which decreases a bit in effectiveness over time. Try to avoid using skillshots against Shyvana until after she casts Burnout, as the movement speed boost, especially at the ability's initial use, can allow her to easily dodge them.
Shyvana tends to jungle and normally, Shyvana's jungle route starts at red. Thus, considering stealing her blue is a likely safe method to take experience away her early jungle and to prevent any enemies from having it.
In her dragon form, Shyvana is more powerful than during her human form.
Beware overextending into tense situations to chase her in her dragon form. Burnout increases her movement speed to make catching her difficult and leaves a fiery trail that can deal significant damage if you do not avoid it.
Following the burning trail allows you to find her easily, but you also take DoT.