When starting a game, make the AI easy and change the categories to only something you know. I personally know pop culture well, so I just left pop culture checked and I finished with a win of $100,000.
To unlock this Achievement, make sure you have at least $25,001 dollars at Final Jeopardy or when you randomly choose a Daily Double. Bet at least $25,001, not $25,000. Just risk that much and the Achievement unlocks regardless of answering correct.
EDIT: It is possible this only unlocks on Daily Doubles.