I finally got it. First off, I'm certain I should have had it long ago, and many times over, so there's still something buggy with this achievement. But let me go over two things.
First off, and this may have nothing to do with anything, but I generally stay online with Steam but offline with Steam friends. When I launch Poker Night, the opening menu comes up almost immediately when I do that. However, if I connect to friends first, it takes an extra 10 seconds during which I get the Win 7 please wait circle. When I played that very first tournament and didn't get any of the achievements that I should have, it was in the former case. Coincidence? Maybe. But, to be safe, I've tried to subsequently be sure the latter was the case. Interestingly, if I go online with friends and then back offline, I still get the additional wait and have received achievements. However, again, this is completely anecdotal.
Second, my getting the achievement this time was under the following circumstances:
- All players were still in the game.
- Both times I went all-in myself before anyone else did.
- Both times everyone at the table folded.
I'm not suggesting this is necessary, I just thought I'd post the circumstances for those trying to maximize their chances of getting the achievement since it is most certainly buggy. Good luck!