Yes, there are moments when April saves the turtles as damsels!
 

In the episode "The Incredible Shrinking Turtles", by dumb luck, April helps restore the turtles to their proper size. Also, in the episode "Superhero for a Day" (somewhat ironic), April herself, thanks to her driving skills, turns off a machine and then unties all four turtles herself! I believe there is another episode or two where April helps rescue the turtles from what I recall.

She got the turtles out of jail in State of Shock.

And at the end of The Day The Earth Disappered, she prevented Dregg from entering the turtles' lair by closing the portal.

And in A Turtle In time, she got the turtles out of the power draining cells by pretending she couldn't breathe.

She also unfreezes Donatello in the second Slash episode.

Doesn't she, Casey, Splinter, and Zack save them in Night of the Rogues?
She and Casey also have some part in Cyber Turtles...I'll have to rewatch it.

She always unplugs the machine / trips on the power cord /removes the batteries too.

This is also a reason why I hated her portrayal in Turtles Forever "We save April at least once a day", sure its a funny line but disrespectful to OT April. Of course she was used as a damsel in distress plenty of times but when you average out that the cartoon lasted more than 100 episodes she really wasn't used all that much for that very reason.

April definitely doesn't get enough credit. Though she often brought trouble upon the turtles, she also helped out a few times, and brought serious biz to the turtles attention that would've otherwise caused great harm to the city. She's a good broad.

I don't know how many time I've told those boys, never call chicks broads. - R.J. Fletcher UHF

I completely agree with this, I hate how so many people call OT April a DID when she could very well take care of herself. There are numerous instances where she saved the turtles asses or acted selflessly to aid someone they were trying to save. I think one example of this is in the Return of the Turtleoid episode where Kerma is being attacked by a terminator robot and she helps Splinter protect him. Best OT April O'Neil moment!

The thing is April was literally fearless. She would throw her life into danger just to get a good story.

I guess its because whenever April did get tied up, she could never free herself and needed the Turtles.

Didn't the Nostalgia Critic leave her out of his Dumb@$$es in Distress video for just the reasons we've listed?

yes, which was a smart move on his part. What irks me the most is when fans compare OT APril to 2k3 April. Ugh!