There are 12 treats total to earn.
Earning treats in adventure mode is quite simple. You just clear enough of certain colors of Yosumin and it unlocks. Then you can go to the "Treats" menu and select it to use its special effect in game. The Yosumin you clear add up cumulatively, and you can see how many you have cleared in the Treats menu.
Big Badmin Choc
800 Yellowmin
Makes Bigmin (giant Yosumin) and Badmin (black spiky Yosumin) less likely to appear
Wing Pudding
3000 Yellowmin
1500 Redmin
1500 Greenmin
Makes more Wingmin (Yosumin with wings) appear
Hint Biscut
1000 Yellowmin
500 Redmin
2000 Greenmin
Gives you an instant hint
Time Herb Cookie
8000 Yellowmin
4000 Greenmin
2000 Orangemin
Increases the amount your time bar refills by (like when you clear a Goldmin)
Color Plus Tramisu
5000 Yellowmin
3500 Redmin
1500 Bluemin
Makes more of your own type of yosumin (The character you choose) appear
Cryptic Crepe
10000 Yellowmin
10000 Redmin
4000 Bluemin
Makes secret bonuses easier to achieve (only need to fill the secret meter to 3, even though it will still show 4 spaces)
Color Minus Jelly
2000 Yellowmin
6000 Greenmin
2000 Dripmin
Makes one type of yosumin other than your own appear less
Corner Cake
2000 Yellowmin
2500 Redmin
Makes your own type of yosumin more likely to appear in corners
Chain Donuts
4000 Redmin
2000 Bluemin
2000 Dripmin
Makes it easier to get chains (gives you 15 seconds between each link instead of just 5)
Target Shrinker Sundae
8000 Redmin
12000 Greenmin
8000 Orangemin
Decreases the target slightly (I'll test some more, but it looks like it decreases all your targets by 25%)
Time-Pop
10000 Bluemin
15000 Dripmin
5000 Orangemin
Makes your time bar go down more slowly (Combine with Time Herb Cookie for epic win)
Angel-Gift Tea
20000 Redmin
10000 Dripmin
15000 Orangemin
Increases the effect of other treats (I'll have to a little more research to figure out exactly how it affects each one)
Also, something I noticed about unlocking some. You start with only Yellowmin in your party (character select). You can unlock Big Badmin Choc because it only needs Yellowmin. But even if you clear enough to earn Wing Pudding, it won't unlock until you get Greenmin in your party. Same goes for any others that require colors that aren't in your party. For some reason though, you can unlock things that require Redmins even when he's not in your party. He is the last one to join you.
And one more note, when you get a game over, you still keep all the yosumin you cleared in your cumulative totals. So if you are only trying to get one color, you can keep doing the same level over and over and failing it each time.
The achievement will unlock once you go back to the world map after earning your 12th treat.
EDIT: sacredskullkid reminded me of this. If you beat the final level, the credits will roll and you will be taken back to the main menu. When you choose to play adventure mode again, you will have to start from the begining. BUT, you still keep all your characters, treats, and total yosumin cleared. Not a huge problem, but you'll have to wait until world 4 before you can clear any more Orangemin again, so if you don't feel like doing that, go for this achievement before beating adventure mode.