This isn't that hard. You have to bet on a single number... like I played for an hour last night betting on 14 (along with other bets). Once I win this achievement I will update on whether or not you can bet on other things too (like 14 AND all black, etc).
NOTE: 0 and 00 count too...
It's a 2.63% probability to win, so this one may take a while. I've played at least an hour straight betting $100.
On a side note, you could try and get as many numbers as you can, and the achievement should pop. (I'll try that asap.)