If Rattata, it would be impossible!!
Why? Rattata is a weak Pokemon and there's no way it can make your Pokemon
dissapear. (Look at the LoG Guide Tool. It makes the story cartoon-like.)
If Giratina, also impossible!
Why? Giratina wouldn't be set to such a low level, as it is a Legendary.
I doubt the "Eyes" are the Pokemon you mentioned above.
It would be a special Pokemon. Maybe it is made by Team Earth or the DO?
(Just like what Team Rocket did with Mew, and failed to copy it, and it became
a whole new Pokemon - Mewtwo.)