Giratina and the Sky Warrior
Giratina first appeared in the 11th Pokémon movie as one of proimary protagonists (alongside with Shaymin), Giratina and the Sky Warrior. In beginning of the movie, Giratina's home world, the Reverse World, was polluted with black, poisonous clouds due to Dialga and Palkia's deadly battle in Alamos Town from the previous movie. This disturbance angered Giratina so much that it decided to get revenge on both of them by battling with Dialga first. When Dialga stopped at a lake to get a drink of water, Giratina lured it through the portal and attempts to engage it in a battle. However, thanks to Shaymin, who unexpectedly stowed away on Dialga's tail, used its Seed Flare move to give Dialga a chance for it to escape and return to its own dimension. Giratina tried to follow it, but it ended up getting trapped in the time loop, which causes it to become unable to move into the real world. Giratina decided to capture Shaymin so it could use Seed Flare again to create a hole in the real world, which in fact shattered Dialga's time loop. Later on in the movie, a greedy and selfish man named Zero, who is planning to use Giratina's abilities to rule the Reverse World, captures Giratina and absorbed most of its powers. Unfortunately, Ash and his friends snuck into Zero's airship and freed Giratina from its prison. After that, Giratina loses conciousness from the energy drainage of its powers but was healed by Shaymin's Aromatherapy. In the climax of the film, Giratina assisted Ash, Pikachu and Shaymin to battle Zero and put a stop to his evil plans once and for all. After the Reverse World was saved from Zero, Giratina thanked Ash and his friends for their help and goes off to continue its search for Dialga.
Arceus and the Jewel of Life
Giratina made its second and final appearance in Arceus and the Jewel of Life. After Dialga saved Pikachu and Piplup from being sucked into a deadly spacial distortion, Giratina appears and ambushes Dialga, still angered for causualities for its homeworld. Sheena tried to communicate with it by reaching into its heart, but due to its anger towards Dialga it was filled with rage. Ash pleaded it to stop and Giratina, who recognized him as the same person who saved it and helped save the Reverse World from Zero, calmed down. Once Giratina stopped attacking, Sheena reached into its heart and told it to return to its dimension. Later, when Arceus came and started destroying Michina Town, Giratina assisted Dialga and Palkia in protecting Ash and his friends from Arceus's attacks. Although it was injured, Giratina was healed by Arceus after the timeline was changed and returned to the Reverse World where it could live in peace once more.
Giratina's personality is hard to determine based on the trilogy of moves where it debuted. What can be known about Giratina is that it's very protective over it's domain and possibly home, the Reverse World. When Palkia and Dialga fought in Alamos Town, the space-time intense variations resulted in the generation of dozens of very toxic clouds over the Reverse World. Giratina probably minded these clouds most because they were damaging to the dimension itself. If Giratina shares with Palkia and Dialga the trait of don't needing to breathe to survive, it would then lack any kind of respiratory system and consequently any kind of weakness to the toxicity.
Giratina seem to be more strategic than it's counterpart Dialga. It probably didn't intervened directly to Dialga's and Palkia's confront in Alamos because it knew that together the two could easily overpower it, just like they did to Darkrai. So, in Giratina and The Sky Warrior, it waited until Dialga come to a lake in it's necessity for water and ambushed it, dragging it to the Reverse World, where it could reverse to it's Origin Forme and get the upper hand on the fight.. Yet, once in the Reverse World, Giratina decided to wrap it in it's constrictor body instead of using any super effective move on it, witch would be Aura Sphere, that Giratina knew. Giratina didn't used any move at all in that occasion.
It showed gratitude towards Ash when he helped saving it from Zero, stopping the fight against Dialga when it discerned that it was Ash's friend. It also showed the capability of keeping past actions in the past, forgiving Dialga for it's fight with Palkia and understanding that Shaymin helped in Dialga's escape accidentally because it was confused and scared, forgiving it as well.
Giratina showed a protective attitude, selflessly taking Arceus's Flamethrower for Ash and his friends in Arceus and The Jewel of Life. Until the end of the movie, it fought Arceus bravely alongside Dialga and Palkia.
Despite being treated for most legends as and betrayer and violent being, and even showing some aggressiveness in the movie trilogy, it seem to lack knowledge about type disadvantage and immunity, as shown when it tried to use Shadow Force, a Ghost-type move, on Arceus while it was still a Normal-type.
Giratina showed the possibility to have a frightening accent, possibly scaring Dialga and resulting in it's getaway. It showed to be also able to keep some resentment, becoming angry with Dialga for the whole time between its escape in Giratina and The Sky Warrior and when it met it again in Arceus and the Jewel of Life.