The Four Kings Casino and Slots

The achievement description doesn't mention it, as it was originally part of a DLC pack and therefore obvious, but this can only be achieved in the Winds of Fortune slot machine. The most realistic way to win 25,000 chips in "one" spin is by betting fairly big and eventually getting 4 Bonus (Koi) Symbols to land in the frame, triggering the Bonus Round. The Bonus Round on this machine is ridiculously gratifying, as it then launches into 8 free spins with extra wilds thrown in, all counting as the "one" spin that launched the Bonus in the first place. A Bet of 5 with Lines set to 100 (somehow 1,000 total chip cost per spin) should make the Bonus pay often (not always) enough for this achievement, but if you want to go for you'll probably want to bet common folk max of Bet 20, Lines 100 (somehow 4,000 total chip cost per spin).

These are risky large bets with no guarantee of paying you back within the number of spins that you expect. You may want to designate these kinds of achievements as a last-ditch-effort way to spend the rest of your chips when you've gotten as much as you want out of the game.