You unlock the ability to swim in the fifth world, Sea of Serendipity.
Exactly the same as "Sprinter!", only instead of running, this trophy requires you to swim a total distance of a "marathon".
Doggy paddling on the top of water does not count, you need to submerse yourself in the water. As you'll be replaying the levels in the Sea of Serendipity for Electoons and Time Trials, you will unlock this trophy naturally.