Pardon the long post, I love talking about Shyvana.
Augments are by far the best option for her passive.
One of the old Ideas I had was to make Dragons spawn in a specific order. Ocean/Mountain/Cloud/Infernal. If the dragon was taken by Shyvanas team, then the next Dragon type will spawn, if not, then the same type will spawn up to 3 times. Augments will not stack.
Dragons taken by Shyvana or her team grants her an Augment to empower one of her abilities and gain a passive respectively.
Ocean: Converts the mana regeneration to Health regeneration. Targets hit with basic attacks marked with Flame Breath are slowed by 20% for 1 second.
Dragon Form: Flame breath now slows targets for 1.5 seconds by 40%
Mountain: Increase Shyvanas Armor and MR by 10/15/20
Dragon Form: Shyvana ignores all damage under 20/50/80
Cloud: Increase Shyvanas Atk speed by 10/20/30%
Dragon: Shyvana may recast Dragons decent once when out of combat for 3 seconds but will only restore 25 fury.
Infernal: Targets marked by flame breath take an additional 50/70/100 damage over 4 seconds. Damaging an opponent resets the the timer
Dragon: Immolate: Shyvanas gains and aura which applies grievous wounds and deals 40/55/70 damage per second.
Elder: All on hit effects are changed to true damage for the duration. Regardless of source.
Dragon: Shyvana’s Total HP is doubled.
Another one was to essentially transform her as she took dragons with a choice.
Shyvana is capable of selecting 1 of the 4 Crest she has acquired.
When activated Shyvana raises to the sky transforms in a flame and descends becoming unstoppable for a distance and knocking up all targets in range briefly. Transforming into a dragon grants her 150/250/350 HP and 125 Attack range and increased size and the bonus of the crest she has obtained.
Each transformation grants unique effects to all of her abilities. Having a crest will retain its passive effect regardless of the form used.
Crest of the Ocean Dragon: HP regeneration is increased by 2x. All healing effects are increased by 40%
Q: All targets are in range are slowed by 30%.
W: Stepping on the burn trail or taking damage causes a slow 20% instead and reduced damage.
E: Hitting an enemy directly before the explosion will stun them for 1 sec. Targets hit with the explosion will be slowed by 40% for 1.5 seconds.
Crest of the Mountain Dragon: Damage under 50/70/100 is ignored.
Q: Enemies struck are stunned for.5 seconds
W: Armor and MR are increased by 15/20/25 and +20% tenacity for the duration.
E: The projectile fragments and deals damage AOE in a cone behind the initially hit target. Shredding an additional 10/10 AR/MR for 3 seconds
Crest of the Cloud Dragon: Fury is increased to 150 Ult can be recast for 25 fury (disabled if under 15 fury) 4 second cool down.
Q: Increase attack speed by 25% for each target champion hit. 5% for minions/monsters
W: Increase movement speed by 100% during the duration.
E: Increase the speed of the projectile and reduce the CD by .5 per AA
Crest of the Infernal Dragon: Passive basic attacks against Shyvana return 20% of the damage and apply Grievous Wounds
Q: Deals a dot to all enemies hit of 70/100/130 damage.
W: Burn trail deals more damage. Burn out doubles in size.
E: Targets take dot damage over the duration they are marked.
Crest of the Elder Dragon: All on hit effects are converted to true damage. Bonus HP from R is doubled. Only available if Shyvana has the buff.
Q: Shyvanas basic attacks are converted to Twin bite. The second attack deals 50% damage at all ranks.
W: Immune to slows/snares/roots while active Increase armor/MR by 20/20
E: Shyvana can charge flame breath for 2 seconds to increase the damage up to by up to double.