25 at-bats.
It can't be 24, because the bottom of the ninth can only be skipped if the team batting then is ahead. At least one batter must be faced in the bottom of the ninth, but if he scores to put his team up 1-0, the game ends after the 25th at-bat.
For a more pedantic answer, 9 would be the minimum number of batters, since at-bats by the same player are still only one batter ;)
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