By lizzyanny from Seattle, WA
I felt like you when I brought in a young female for a companion for my older male desexed cat. It took well over 6 months for them to even tolerate one another. After being together three years there seems to be a sort of friendship.
Jannieb's advice is spot on. New kitty is just doing what her instincts are telling her. I would like to add that a spray bottle filled with water set on "stream" would be handy if she continues on with the Top Gun behavior. It might prevent an attack and give her something to ponder.
Give them time. It can take up to 2 months or more for the cats to get adjusted to each other. In the meantime give the new cat a safe haven like a spare bedroom with a litter box & let them adjust at their own pace. Believe it or not they will eventually like each other!
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