Yveltal is a legendary Pokémon from the Kalos region, who was well known for its ability to absorb the life force from living things when its life span was about to end. 800 years prior to the events of X and Y, Yveltal engulfed the land of Kalos with a darkness emanating from its wings. This caused all of its denizens to slowly weaken and die, resulting in catastrophe. After it had absorbed enough life force, it took to the sky, disappearing to an unknown location.
In reality, Yveltal retreated into a cocoon to restart it's life cycle, which was eventually discovered by Team Flare and transported to their lair underneath Geosenge Town. It would be harvested for energy to fuel the plans for the crime organization, however this plan was to recreate the Ultimate Weapon, which Lysandre had planned to use to wreak havoc across the entire planet. just as it had thousands of years ago in the Great Pokémon War.
However, through the heroics of the protagonist, Yveltal was awakened from its cocoon and was caught, before being used to battle Lysandre, defeating him. The machine, still powered with Yveltal's energy, was set off by Lysandre targeting itself, destroying the entire Team Flare lair and their leader along with it.
Yveltal has been flying above the forest in search of stealing the trees' life force since it was almost the end of it's life span. As it landed on the ground, it prepared to steal the life force by using Oblivion Wing on the trees. But before Yveltal could used the move successfully on the trees, a blue pulse attack was heading straight towards it. Thinking fast, Yveltal quickly dodge the attack, and flew up high to find the Pokemon that tried to attack it.
Then suddenly, a Rayquaza had descented the from sky, roaring at Yveltal for entering its territory. However, Yveltal wasn't easily frighten by the roar and refused to back down without a fight. Yveltal tried to fired a dark blast from it's mouth at Rayquaza, but its opponent easly dodged the attack. Yveltal tries to chased after Rayquaza while trying to keeping using Oblivion Wing against its target, but Rayquaza keeps dodging the attack without any effort.
Then Rayquaza fired a blue pulse at Yveltal, causing it to fell into the ground. Then Rayquza chased after its opponent, not wanting to give its opponent the chance to fight back. However, when the dark aura surrounded its body, Yveltal disappeared without a trace.
Rayquaza had no idea where Yveltal, and was forced to looked for it. Unknown to Rayquaza, it was suddenly rammed by Yveltal just shortly after revealing itself. Just was Yveltal was about to used Oblivion Wing to finished it off, Rayquaza quickly dodged it at the last moment berfore the attack hits it.
Then it used Ancient Power to attack Yveltal, causing it to take much damage. Then it finished it off by firing a blue pulse at Yveltal, causing it to take much more damage in battle. Realizing that it would not win against Rayquaza, Yveltal began to flew away from the battle before things could turn in for the worse for it. Having to finally realizing that Yveltal would no longer be in its territory, Rayquaza roared in victory before ascending back into the sky.
While Yveltal's moves prove to be hard, Rayquaza was able to dodge its attacks due to its body style, and if that wasn't enough, Rayquaza was able to took on two Legendary Pokemon on its own.
Yveltal was in the Reverse World, on the search for more energy to feed from the Pokemon. However, there was something not right about this place. It didn't seem to have Pokemon in the place. However a electricity attack quickly heading toward Yveltal, but it dodged just in time before the attack hits it. Yveltal then saw that Giratina was behind the attack. Yveltal roared at Giratina to stand down, but the Dragon Pokemon wouldn't back down. Yveltal's claws began to be covered in flames before trying to attack Giratina with it. However, Giratina used it's tentacles-like claws to defend itself, and hit Yveltal on the spot. Then Giratina disappeared by the using the power of darkness.
Yveltal tried to look for Giratina, but it was confused about the place. Then all of a sudden, Giratina hit Yveltal on the spot causing it to fall on the ground. Furious at Giratina for causing a sneak attack on it, Yveltal fired a Dark Pulse attack on his Opponent. The attack hit Giratina successfully, causing it to take a lot of damage.
However, just as Yveltal is about to deliver the final blow to his opponent, Giratina zapped his opponent with a Thunderbolt, shocking Yveltal. Yveltal tries to attack Giratina, but it was paralyzed, preventing it from taking action.
Knowing that Yveltal can't move, Giratina proceed zapped it's opponent with another Thunderbolt attack. Couldn't take another attack anymore, Yveltal has become fainted. Realizing that Yveltal was unable to continue, Giratina roared in victory over his opponent.
While Yveltal has the type advantage over Giratina, it doesn't know the Reverse World well. In addition, Giratina was even more powerful in the Reverse World. The tentacles-like claws is able to protect Giratina from Dragon Claw, and knows in the Reverse World better than Yveltal.