STORY OF SEASONS: Pioneers of Olive Town

After a few days of rain, Clemens, the town mechanic, will offer to give you a bucket to clean up some of the puddles on the farm. Using this bucket will allow you to scoop up the water, tossing it away and getting some clay in reward for your efforts. You'll need plenty of clay later on for some upgrades, so it won't hurt to keep them around. You can also use this to help clearing out some smaller or bigger lakes that will form from the second area on. I do not know if it counts instances of pulling water out of the lakes. If you'd like to check your progress on this trophy or others:

1) On the Title Screen, go through the trophy icon to find all tracked trophies. Trophies with cumulative progress can be tracked from here.
2) In-game, go to the Records page of your menu and choose Change Title. Interact with the Draining skill and you'll be able to track the amount of times it has counted. You'll see tons of puddles throughout your game anyway.