Without a doubt Beatrix Kiddo, central character of KILL BILL Parts 1 and 2, was the most notable femme formidable to debut in 2003.
In large part the character derives from the cinematic version of the manga character Lady Snowblood, discussed in this post. In contrast to the manga series, which emphasizes Snowblood's career as a professional assassin prior to setting her on the road to revenge, KILL BILL barely touches on Beatrice's assassin-career. Like the 1973 film the narrative action concentrates entirely on the revenge theme.
There are still significant differences, however. The Snowblood character becomes an assassin because of her parents' ill-use by exploitive criminals, individuals who care nothing about her or her family. We don't know how Beatrix becomes an assassin, though there's a minor suggestion that she may have been brought into the trade because of her romance with Bill, master of a gang of mostly female assassins. One scene from KILL BILL PT 2 shows Bill and Beatrix comporting themselves as lovers just before Beatrix seeks training from Bill's old kung-fu mentor Pai Mei. However, when she becomes pregnant with Bill's child, Beatrix decides that she wants out of the assassination game, and fakes her death to escape Bill's influence. But he tracks her down, and after letting his other female assassins beat the crap out of Beatrix, Bill attempts to blow her brains out. She survives to pursue revenge-trail on the persons who had been nearest and dearest to her (with the likely exception of Elle Driver, a female assassin who clearly envied Beatrix's relationship with Bill).
Since the spectacular martial-arts scenes of the first film have been lauded by thousands before me, I won't bother repeating that mantra. The second film places less emphasis on action, devoting more time to a character study of the dysfunctional relationship of Bill and Beatrix, not to mention incorporating writer-director Quentin Tarantino's meditations on the nature of heroism.