Starting on the fourth level after you kill a few monsters and unlock a few doors, you will occasionally see slot machines. Once you see one, go up to it and begin putting money in.
Each of the three slots has seven possible options: cherry, coin, bar, triple bar, bell, bunny, and the number seven. You need three sevens for this achievement. As far as I can tell, which one shows up each time is generated randomly, meaning the odds for a seven in an individual slot is a little over 14% (1/7) and the overall odds of getting what you need (three sevens) is roughly 0.3% (1/343).
Each pull of the slot costs $10 and takes around five seconds, meaning this should take around $3430* and 30 minutes. There is no way to increase your odds, but just keep trying and you should get it eventually. Good luck!
* You will hit slot pulls that garner you money in this process (for instance, I got three bells along the way, which provided me an additional $5k); I did not factor this in to the $3430.
Note: These are just statistics, not guarantees. I provided them to give some insight into the average-case cost and time investment necessary for the achievement. Results will vary because the slot pulls are random.