First I can think of is Ellen Ripley from Alien and Aliens. Didn't start out badass or ass-kicking, but sure as shit ended up doing so.

If only that era of movies hadn't spawned a TV Trope that sadly coloured these folks' perceptions on strong, independent, rough and tumble women: https://tvtropes.org/pmwiki/pmwiki.php/Main/VasquezAlwaysDies

Battletech does indeed have its long list of badass action babes, the top eight entries of which are Natasha Kerensky, but you've also got the likes of Melissa Steiner, her daughter Catherine "Katrina" Steiner-Davion, Dierdre Lear, and to a degree Isis Marik. A lot can be said for the women of the Draconis Combine as well who aren't permitted to be warriors but tend to politick and intrigue a lot, such as Omi and Constance Kurita.

Pulling just two examples out of that list, Dierdre Lear is a pacificst who became a doctor and jointed the military as a MASH trauma surgeon. Her father died in a 'mech duel when she was a little girl, and so she decided she was gonna fix war one bandaged gunshot wound at a time. She serves during the Clan invasion, being swept along with Kai Allard-Liao in his adventures, first kind of inadvertently causing and playing a significant role in the Twycross Great Gash incident by objecting to moving her MASH unit, and then on Alyena becoming trapped behind enemy lines and forming a one man one woman insurgency with Kai. She shoots one man in the back to save Kai's life and is deeply conflicted by this action.

Constance Kurita is a cousin to the Coordinator (dictator) of the Draconis Combine (space feudal Japan), In an oppressive society that doesn't like sending women to school, she joins the Order of the Five Pillars which is kind of what this society has instead of scholar monks, eventually becoming the Keeper of the House Honor. As such she has an intelligence network that rivals that of the military's intelligence service and often shares moments of "I can't tell you how I know this but here's something you should know and what you should do about it" with her cousin Theodore, heir to the throne and often in positions of power; as Theodore rises through the ranks, so does Constance and her influence and reach often matches his. She's not the captain of the ship of state but she's definitely got a hand on the tiller and a better idea of what's going on in the engine room than the bridge crew does.

Battletech actually did that kind of thing well, sure there's plenty of Rambo action schlock, it is a series of novels designed to market a tabletop game after all, but they put some craftsmanship into it.