I just had this experience with Ria. I was totally unimpressed with the other Companions in battle, so wasn't really expecting much from their second-newest member.
So we clear out of Whiterun and pass Valtheim Towers, where the bandits are looking for a fight. If you've cleared it out before, you know there is the main tower with a long, narrow stone bridge going across the river connecting it to another tower in the mountain. So I'm at the beginning of the stone bridge, facing a bandit archer or two that I am going to Fus Ro Dah off the bridge to their deaths, as I had done to their comrade on the top of the tower.
Then, in typical follower fashion, Ria gets in front of me right as I shout -- and she is thrown off the tower with the other two, almost certainly to her death. I look below as she hits the ground, fully expecting to watch her lifeless body get pulled down the river, as the other two are. But as I watch, she gets up like it wasn't a big deal that she just fell three stories, and shakes it off.
I run down to the banks of the river to see if my eyes were deceiving me -- but no, I saw correctly. Then, as I'm standing there, dumbfounded, on the banks of the White River, Ria runs back up the tower, across the stone bridge, and fights off the last archer perched on a rock on the other side of the bridge.
I had expected so little and was thoroughly impressed. I want to hear your stories of improbable badasses in battle.