If you don't want to cheat, there is an easy enough way to get this without following the submerge-then-pause route:
- Enter or create the tutorial world (the way it is at the time of writing this, June 26, 2017; I'll update this later if necessary). Skip the basics tutorial and go through to the main area.
- Find the brewing stand (it's indicated by a water bottle in an item frame, on the right-hand side just after you cross the entry bridge. You might like to note that you can also take that bottle if you need it). Brew an Awkward Potion from the available ingredients using Blaze Powder, a Water Bottle (fill one from the nearby cauldron if you need to) and a piece of Nether Wart.
- Leave the Awkward Potion sitting in the brewing stand while you go over to the fishing quay, which is towards the left side and a bit further in, accessible either through the vegetable farming area or past the villager with the anvil.
- Take the Fishing Rod from the chest or item frame on the quay and fish until you hook a Pufferfish (they look like yellow suns with faces).
- Take the Pufferfish back to the brewing stand and add it to your Awkward Potion. This will create a Potion of Water Breathing that will last for 3 minutes, which is all you really need (though it is possible to extend the time to 8 minutes, if you prefer).
- Take the Potion of Water Breathing to the quay, drink it when you get there, and hop into the water. Sit in one of the deep parts of the water (over your head) for 2 minutes (you can check how much time remains on your water-breathing enchantment by viewing your inventory, or just wait until your air starts to run out).
- Achievement unlocked! Don't forget to come up for air when you're done. ;)
For the tl;dr crowd:
- Go into the tutorial world.
- Make an Awkward Potion at the brewing stand (Blaze Powder, Water Bottle, Nether Wart).
- Go fishing for a Pufferfish from the quay.
- Bring the Pufferfish back to the brewing area and add it to the Awkward Potion.
- Take the resulting Potion of Water Breathing (3:00) to the quay, drink it, then sit under deep water for 2 minutes (you can check the time remaining on your current potion effects by looking at your inventory).
- Achievement unlocked. :)