Very easy, you need to need to stay under water for 2 minutes by using either golden apples or a water breathing potion. The Notch Apple world works pretty well for this. Simply craft the apple with the 8 golden blocks and the apple to unlock the notch apple achievement. Then Head to the water, be sure you're underwater entirely, and then eat the apple once your oxygen is about to run out. With the effects of the notch apple, you will be able to stay underwater for 2 minutes.
If you're unsure how to get the worlds onto your PC/android/ios device, the following forum I started might help, otherwise there are plenty of youtube videos.
Achievement worldsYou can download the Notch apple world from here:
https://www.dropbox.com/sh/v6ggssr1ag7uerp/AACU3QfRen68hOMno...