The issue with the movie is that it follows the damsel in distress trope.

The issue with The Perils of Pauline is that it was written and performed by people 50 years dead in an era concurrent with the Model T. The issue with Read Dead Redemption is that it was written and performed by people in an era where singling out any minority group for persecution is socially deviant.

You don't get to put on blackface, no matter how hilarious you think it is.

Forget the whole fact that through most all games nearly all those who are killed, in both situations of helplessness and of not, are men.

No, focus on that. It emphasizes the unusual nature of killing - specifically - a woman.

What does it say to take offense to this one achievement just because it involves killing a woman in a senselessly violent way?

That it's not okay to specifically kill a woman in a senselessly violent way.

Because I see it as the very thing that is wrong with the trope in the first place.

There is no "trope." There's only "100 years ago."

The idea that women should be protected, shielded from violent action, and that they can't stand up for themselves.

This is not "defeat a woman in battle." This is "find a defenseless woman and kill her."

I am still saying that it is not a valid point, no matter how many times you tell me I am mistaken

It is abundantly clear that you view your arguments as valid. Wishing does not make it so.