Alternatively, you can use magma blocks underwater (since they create air bubbles). Note that you cannot swim over magma blocks as you'll sink to the bottom and that walking on them will damage you.
Place (or find) some magma blocks underwater. Put a non-damaging block on top of one of the magma blocks. Stand and crouch on that block and move so you're hanging over the side. You'll get air from the bubbles and won't take fire damage.
When the achievement pops, move to the center of your block, uncrouch, and ascend straight up.
Note: In the tutorial world, there is a magma vein to the southwest of the map.
Note 2: Bring a clock to get a sense of what time of day it is and how much longer it will be before the achievement pops.