This is a pretty straight forward achievement. You can unlock this very early in the game if you want to. Simply go to a body of water, jump in, and press RT to dive. Once underwater, tap the A button to swim deeper and make sure you do not resurface before running out of breath.
Once the breath meter runs out, you will start to lose health. As soon as your health meter runs out, you die and the achievement will pop immediately.
Alternatively, you can drive a car into a body of water and wait until you drown, which is even quicker and easier.