The answer to this question is exactly as straightforward as it is for some other stories. In general, the narration stays firmly in the third person. I'd like to say that the narration is 100% omniscient; however, that isn't the case. Readers do get to see inside the heads of many characters other than Ender. The start of each chapter gives readers some insight into what Graff is thinking and doing, and we do get quite a bit of Valentine's thoughts. But, interestingly, readers never get a look into what Peter or Bonzo feels. We have to learn Peter's thoughts and motivations through his actions and what he says to Valentine. Finally, there are moments when the narration flirts with a first person perspective. Notice the following few lines.
Father and Mother said it, so often it made Valentine want to scream at them. It isn't the new Peter! It's the old Peter, only smarter!
How smart? Smarter than you, Father. Smarter than you, Mother. Smarter than anybody you have ever met.
But not smarter than me.
The italicized part is definitely third person, but by the end of the quote, readers are in Valentine's head.