Action heroines are rare creatures. The earliest were female versions of pre-existing male heros, like Wonder Woman, BatGirl and SuperGirl. Some more recent heroines have their roots in fantasy or sci-fi, like Buffy The Vampire Slayer, Selene from Underworld, or Alice from Resident Evil. But while there are plenty of realistic male heroes who run, jump and fight without being cartoony or existing in a vampire realm - think Jason Bourne, James Bond or Ethan Hunt - there are very [few] female counterparts.
Maybe so. But I think there have been some awfully good ones. Off the top of my head and in no particular order: Sarah Walker. Samantha Caine. The Bride. Mrs. Smith. Evelyn Salt. Nikita. Erica Bain. Sydney Bristow. Grace Hanadarko. Mary Shannon. Pretty much every character Michelle Yeoh's played. Ditto re Pam Grier. All wonderful action characters at least as "realistic" as Jason Bourne or James Bond (and most of them could probably kick Biond's butt).
And what's wrong with SF heroines? The iconic Sarah Connor. The great, great Ellen Ripley. Emma (be still my heart) Peel. Xena. Trinity. Starbuck (reimagined). Abby Maitland. Dana Scully.