As the description says, you can earn this achievement while playing online or in single player mode. At first, I thought I could do it in single player mode, but I got lazy and stopped paying attention around game 15, at which point I would do something stupid and lose. Then I decided to try to boost and win a bunch of games by trading 25 wins with a friend. We tried speeding it up by using the doubling cube, but that didn't work. My guess is that Silver Creek Entertainment issued a patch that prevents it. So, I went back to single player mode and actually paid attention for 25 games... I found that beating the Easy AI (when paying attention) got me 25 wins easily.