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Maybe Not so Fast, Bucko! ?
"Your kindness gives me the presentiment I can be reborn. Now, I want to believe at least in you." - Kaori Yae
Or possibly Hope Spot?
Those sound close to it. As I'm imagining it, though, it's not particularly fight-related, and the character often looks a bit proud of herself/himself, so that we can have Pride Before a Fall — although, at the same time, the pride may be well-earned, and the point of the trope is to show just how darn difficult the task was. (Or just to mess around with the audience's expectations.)
Something bad is threatening to happen — say, a big mess because of a stack of pies is falling over. A character puts in a heroic effort to prevent it, wheeling about here and there. He's successful! Crisis averted! Oh, wait, he missed that one thing happening over there. No… no… no… Ka-rash! A failure.
An example of this would be in the film of Prince of Persia: the hero has to keep any and all rocks from touching the floor, he makes a big show of catching a big one, and another small one immediately comes down. Is there a page for this?