Birdy the Mighty/Awesome

Birdy, in the first episode (of Decode), in the course of catching a fleeing spaceship, forces her way onto the bridge...by punching through its wall. Its outer wall, as in, on the other side of which is outer space.
Again in the first episode, Birdy approaches a criminal posing as a hopeful idol/star -- while the criminal himself is posing as an entertainment mogul. After bursting into fake tears when he tries to brush her off, she suddenly stops crying and looks up at him, calling his name in a low, teasing tone.
- And in the same fight, when the bad guy attacks her, she casually sidesteps the assault, and offhandedly remarks that the bad guy's prison sentence has risen by 5 years.
At age 10, while undergoing training as a federal police officer, Birdy finds herself in the middle of a major terrorist attack. During this, partly in response to her lifelong guardian being destroyed, revealing the guardian to be a robot, Birdy completely annihilates a giant Berserker mecha with her bare hands.
- Extra credit for this being revealed in a flashback in the second season, while she had been called Berserker Killer since the first episode. The prosecution in a trial during the first season even assumed it was referring to a short temper.
In a fit of rage, Birdy (in her idol-star disguise) punches a note left on a wall to tease her. The wall subsequently crumbles, leaving her (again, in her celebrity form) visible to the occupants of the next apartment over.
The fights between Nataru and Moss, and then Nataru and Birdy, in the last episode of season 2 certainly count as CMOA, even if the art quality doesn't.
- YMMV of course. To some, the art is part of the reason it's a CMOA