Gunbuster the Movie (2006)

When alien nightmares attacked humanity's push into interstellar space, Noriko Takaya's father sacrificed himself to stop the advance. What he bought for mankind was time. Time to create a weapon capable of stopping the monsters once and for all. Now that weapon is nearly ready and a teenager Noriko is determined to be in the battle, though it's not until she models herself after the top pilot candidate Kazumi Amano that she discovers her own abilities. However, even as Noriko and Kazumi become both partners there's one aspect of this war that will affect them unlike any other: Pilots traveling faster than light experience time differently than those left on Earth. That means even if Noriko survives each battle, home will no longer be the same place!