To do something in one fell swoop is to do it suddenly or in a single, swift action. Fell here is an adjective meaning fierce, savage, cruel, or ruthless.1 This sense of fell is otherwise archaic, preserved mainly in this idiom. The swoop in one fell swoop is a noun referring to (1) a blow or stroke or (2), metaphorically, a bird’s sudden, sweeping descent from a height.2
It’s possible to imagine contexts where one foul swoop might make sense, but these must be rare. Foul can mean evil or offensive, and some swoops might indeed be evil. Still, one foul swoop is usually just a misspelling of one fell swoop.
There’s also one fowl swoop, which, believe it or not, does appear several times in searches covering recent news stories. This likewise doesn’t make much sense. Some fowl do swoop, but fowl generally doesn’t work as an adjective.
The earliest documented instance of one fell swoop is from Shakespeare’s Macbeth (1605):
All my pretty ones?
Did you say all? O hell-kite! All?
What, all my pretty chickens and their dam
At one fell swoop?
Here, Shakespeare clearly means swoop in its second sense (i.e., a bird’s sudden, swift descent), but the phrase is sometimes used with swoop being closer to its first sense.
The board could have listened patiently, collected its thoughts and forcefully addressed that hyperbolic message in one fell swoop. [New York Times]
The only winner was of course French president Nicolas Sarkozy, who achieved his dual agenda in one fell swoop. [Financial Times]
Waiting at the checkout may not be everyone’s idea of fun, but it’s a way to get your shopping sorted in one fell swoop. [The Age]