In the manga, which sets up a lot of the anime episodes, we have the famous 'arm wrestling' competition. It's well known by now that Natsumi is super strong; the second page of the manga had her move a car with ease. But she has to go up against the entire male half of the Bokuto precinct. Surely she'd get winded after awhile. She does. But even so, by her last match with the chief himself, she's still able to keep the game going for a long time, and when the chief realizes winning means taking her hand in marriage, he forfeits. Keep in mind, there was a large crowd of people watching and participating, and Natsumi had no time to rest in between rounds. She was able to go up against her entire precinct's male (who were in peak condition, while she was slowly tiring) population and win, and even though the chief had to forfeit, it was heavily implied if not outright stated that, had she had time to rest, Natsumi would have kicked his ass too. Natsumi is a badass.
Oh so many, but the poster example is when Miyuki, together with Natsumi and Nakajima who are riding in tandem, take down the rogue officers who were running people off the road and broke Nakajima's leg and Natsumi's arm earlier.
Oh, not just that. As said above, Nakajima broke his leg and later Natsumi broke her arm while trying to catch the rogue officers that caused accidents. They don't want to stay aside in that very difficult case, so they Take a Third Option via getting a specially outfitted motorbike (by Miyuki) that lets both of them drive since Nakajima is in charge of the steering wheel with his hands and Natsumi manages the pedals with her legs. And they rock at using it.
Nakajima jumping off a bridge to save a drowning girl.
Miyuki gets one in the first episode of second season where she fires paintballs onto a moving truck's windshield, from her own moving car, between the pillars of an overpass above them!
Any time Miyuki whips out her sniper rifle, really.
Oshou-san aka Fox when cornered...reveals his car has a fifth wheel, which allows it to turn sideways. Also a CMOF.
Nakajima gets one in 3rd season when he singlehandedly disables the car belonging to a pair of robbers without damaging his bike or himself. Even during his "finishing move," you can see a pair of white wings sprout from his bike.
Aoi's introductory episode has her rescuing the little brother of a girl who adored her in the past, gaining the respect of the Bokuto officers in the process.
Kachou gets two episodes of awesome in the first season, via managing to survive when trapped atop of Tokyo Tower in a VERY windy and dangerous day. And also shield a little child who's trapped with him.
Miyuki and Natsumi's final confrontation with the Scooter Lady. The latter attempts to cow the two with her usual condescending tone and sheer force of will. It doesn't work however as the duo use the same tone back at her.
This is especially awesome as we see the duo from the Scooter Lady's figurative point of view at that point and they absolutely tower over her. Contrast this to the previous encounters with her where she was always able to get her way.
In Episode 2 of the live action series: Nakajima on his motorcycle vs. a hijacked bus. Nakajima wins.
Nakajima's Heroic Second Wind in the third episode of the live-action series where he climbs into Miyuki's apartment to save her from a stalker who has her at knife point. This is also while he's still bandaged up from his motorcycle accident after said stalker had cut his brakes to try and Murder the Hypotenuse.
Natsumi vs. The Heavy Bob Clamp. She's defeated and ends up with a broken arm. Natsumi vs. Bob Clamp round 2 while still having the broken arm: She wins!
In the final episode, Natsumi taking down a gang single-handedly because it was the best way for her to vent her anger at one of her friends being the victim of a hit and run.