There's only one thing you need to understand about boku. Don't watch the anime
Unrelated but I lost my virginity while watching that anime, and this is 100% not a joke.
What anime are we talking about? I searched and found a dozen with boku in their names.
I personally think of Bokurano, the title of which means "Ours" in Japanese.
As for the pronouns, "Atashi" is a cute and feminine pronoun mainly used by girls, an abbreviated form of the somewhat more formal "Watashi." "Boku" is a somewhat polite personal pronoun used by males, usually young or teenage boys, or by tomboyish girls. "Ore" is a rough and rather informal first person pronoun that is used almost exclusively by guys- the only girls who tend use it are either very rude or pretending to be guys.
With that in mind, we know Teruko uses "Atashi," but what does Doujima Taiga use- "Ore"?