Walk up to a soda machine and buy a soda. Rinse and repeat. Press to buy the soda.
The easiest way is to buy them at the Yum-Yum grocery store, as you get to skip the drinking scene. When purchasing them at the store, you can just keep pressing until the achievement unlocks.
**You can check how many sodas you have drunk:**
Start---> Stats---> General---> Objects & Items---> Sodas Drank