Suddenly; in a single action.

This is one of those phrases that we may have picked up early in our learning of the language and probably worked out its meaning from the context we heard it in, without any clear understanding of what each word meant. Most native English speakers could say what it means but, if we look at it out of context, it doesn't appear to make a great deal of sense. That lack of understanding of the words in the phrase is undoubtedly the reason that this is often misspelled - 'at one fail swoop' (or sometimes, stoop).

So, what's that 'fell'? We use the word in a variety of ways: to chop, as in fell a tree; a moorland or mountain, like those in the northern UK; the past tense of fall, as 'he fell over'. None of those seem to make sense in this phrase and indeed the 'fell' here is none of those. It's an old word, in use by the 13th century, that's now fallen out of use apart from in this phrase and as the common root of the term 'felon'. The Oxford English Dictionary defines fell as meaning 'fierce, savage; cruel, ruthless; dreadful, terrible', which is pretty unambiguous.

Shakespeare either coined the phrase, or gave it circulation, in Macbeth, 1605:

MACDUFF: [on hearing that his family and servants have all been killed]

All my pretty ones?
Did you say all? O hell-kite! All?
What, all my pretty chickens and their dam
At one fell swoop?

The kite referred to is a hunting bird, like the Red Kite, which was common in England in Tudor times and is now making a welcome return after near extinction in the 20th century. The swoop (or stoop as is now said) is the rapid descent made by the bird when capturing prey.

Shakespeare used the imagery of a hunting bird's 'fell swoop' to indicate the ruthless and deadly attack by Macbeth's agents.

In the intervening years we have rather lost the original meaning and use it now to convey suddenness rather than savagery.