Sea of Solitude

Load chapter 6 part 1, climb to the top of the skyscraper. You'll descend a big ladder and Kay will make a comment about how she recognizes the furniture. Go up the wreckage by the chairs and you will see a long set of vents. Let them blow you off the edge and the achievement will pop. At least it did for me. Chances are high you will also pop the Comfy achievement, which is where you respawn on those chairs.
This achievement was at 99% during most of my playthrough and I had to reload the chapter after finishing to get it.

UPDATE: (Thanks Calex dEUS) It has been reported that you should intentionally jump off the ledge, not let the fans push you. I don't exactly remember, it's been a year since I played this game, but if it helps people pop the achievement try pressing A to jump off the fan ledge.

Chapter 6-1 (Hurt, The Depths)

You must jump from a high point and hit the water.

The trick is that you have to do it from exactly the right height and must touch the surface of the water with your dive. If you do it from too high up the tower, you will teleport back before hitting the water and the achievement will not pop.

When mine popped, I could see my character just hit the water as the game teleported me back up to where I had jumped from.

I am including a screenshot of the exact ledge I jumped from. My character's back is facing the ledge. The ledge is between 1/4 and 1/2 of the way up the tower from the start of the chapter. It only takes about a minute to get there (from the spawn) if you already know how to traverse the tower.



Press to leap off that ledge, away from the building. I'm not sure if the leap is required but that's what unlocked it for me. If it doesn't work the first time, try it from the same ledge in different ways: falling without jumping, or jumping out further. The height from the water below must be exactly right.

I got this one after being blown off the skyscraper by the vents just past the father's office.