This achievement requires you to be really really REALLY good at chess, because not only will you be up against 5 people in a row who really like chess (like me), but worse, you'll be up against THEIR CHESS ENGINES. So you neither need to be really really REALLY good at chess, or you need to be able to make friends super easily. (I can do that, too.)
OR...You can do it by yourself.
[crickets]
Yes, you can, in fact, solo boost this on one console. However, it may not be how you're thinking.
First of all, you're going to need access to 31 additional accounts...
HEY! DON'T LAUGH! GRAW boosting was serious stuff!
The important thing about the number 32 is that it
just so happens to be the same number as the maximum number of gamertags you can have on your console at one time. (FYI, you can only have 16 logged in at once, if you didn't already know that. I knew that too, but anyway.) And since you have Xbox Live, ALL OF THEM DO, TOO! It's not like the old days on the 360 where we had to get a free or $1 month on those new accounts!
If you don't have 31 alt accounts lying around, well, that's not all that weird, actually. Just get a few friends and share the load. Make some email accounts at Gmail or Hotmail or pickyourfavoriteemailsite.com. Then register them on... okay, so it might be a little bit harder if you don't already have 31 alt tags set up. So, go with the everyone-has-a-few-tags method.
You should be friends with all of these newly minted fake-people so that you can do the next part, which involves you and your new friends joining a 32-person tournament that you set up and fill with these 31 pseudo-individuals. You also should note that the game needs to know that these not-quite-alive beings have access to the game, so you should have them play the game a little. I had all my critters run a pawn forward against the Novice AI and take a knight that they usually just left there. Now you just have to do the tournament!
Here's the kicker... none of you has to actually play the games! A lot of the delay in this game is actually in loading the games, but once your accounts have the game on their tags, that's most of the work! So what about those accounts?
1: Create a 32-person tournament. Select all of your mostly-dead-with-funky-Xbox-tags-like-TurtleSpit32 people. Make sure that at the bottom right of the screen, it says that you've selected all of them.
2: Log all of the tags in...and have them go to the Tournament page and delete your brand-spanking-new tournament. Deleting the tournament automatically forces them to resign, and their opponent wins the game. (Note that if you don't actually look at the bracket, the game may give you a friendly note that there's a server error. You probably don't have a potential opponent on the other side of the bracket yet. It's okay. Keep the tag logged in and come back to it. It'll be fine.)
3: Once an alt has logged in and deleted the tournament, you need to sign in another user. Go to the main screen, press
and switch tags. You don't have to leave the game to do this.
4: Make sure that YOU ARE THE ONLY ACCOUNT THAT DOESN'T DELETE THE TOURNAMENT. Now, that seems like common sense, but hey, I'm not judging here.
5: You actually do need to go back and look at the Tournament page for your achievement to pop. And it will, with an obscenely low % of people who have this. Because none of them has 32 tags lying around, do they?
7: Profit.
(And yes, the same method works for the 20 tournament achievement, too. Just use 4 accounts and make 3 tournaments at once. Quitting out works wonders... I went from 5 to 20 tournaments in 10 minutes.)
Hope this helps!