Alright, in her titular book series, she starts out as arguably the best tactician in the known universe. And still just a junior grade captain. She stops the People's Republic of Haven (Peeps from here on) from launching not one but two surprise attacks. Then, when the Peeps openly declare war, she is the one who suggests and adapts the long-abandoned missile pods for use. For the rest of the war, missile pods play an important role. Capitalizing on this, she later develops the two weapons which win the war for Manticore: Light Attack Craft Carriers (CLACs) and hollowed out super dreadnoughts filled with deployable missile pods (SD(P)s).
She also defeats multiple assassination attempts (the first few just ones she's present for, not ones aimed against her. They are, however, aimed against her once her worth as an officer becomes apparent) by, respectively, beating the crap out of a huge number of would-be assassins (did I mention she's a black belt in Coup De Vitesse?) who were attempting to kill Protector Benjamin of Grayson (for which she's offered a Steading on Grayson, making her essentially a head of state, answering only to Benjamin, and also entitling her to become a countess in her home system of Manticore), kills a professional duelist in a legal duel by firing her pistol from the hip, survives a shuttle crash, escapes from the Prison planet Hades, and intercepts a missile heading for the Queen of Manticore's ship with her own ship (the physics of this universe mean that, since the ships are propulsed by bands of stressed gravity, she could pull it off. It's less complex than it sounds), for which she's made a Duchess.
That's not to say she escapes unscathed. The first assassination attempt she thwarted ends with her losing her left eye and the functionaliy of the nerves on the left side of her face, killing the duelist was in retaliation for him killing her lover in another legal duel, and in escaping the prison planet she loses her left arm. But she turns most of this to her advantage, getting replacement nerves for her face, getting a prosthetic eye (compete with telescopic and night vison), and getting a prosthetic arm, in which a pulser (gun which fires explosive dart) is implanted and completely hidden. Simply put, she's a badass.