Four characters can earn this achievement: the Child and the Student can earn it on part 11 of the Box Storage Area, the Gentleman can earn it in Infinite Mode, and the Duplicator can earn it with luck.
If you are using the Child, start on Box Storage Area, part 10, and at the start of the level transition between parts 10 and 11, jump (or you can jump from one of the boxes). You will notice that the level keeps getting bigger at about the same rate as the Child is falling, meaning he can keep aloft until the level stops getting bigger. Just be sure to land somewhere, or the achievement won't count. Alternatively, at the beginning of Box Storage Area part 11, fall into the gap between the two boxes in front of the Child at the beginning of the level and move left or right to catch onto the side of either of the boxes. The Child will be standing on a box halfway up the wall of the tunnel, and then it is a simple matter of floating down onto a surface, as the height will be sufficient enough to keep the Child airborne for ten seconds.
If you are using the Gentleman, try to enable your electromagnet when you're underneath a power cell, and use the power cells as a "bridge" to stay aloft for 10 seconds. A tip is that when you are going towards a power cell, you can release the electromagnet, then engage it again when you are below the power cell to get a lot of height out of nowhere. This takes practice to pull off consistently but is actually very easy with some practice.
If you are the Student, do the same as the Child, but when you are about to hit the ground, hold space, and you should float to the other side of the level. You can only do this starting on Box Storage Area, part 11, by falling onto the side of a box. Doing the trick at the end of Box Storage Area, part 10 will not work.
You can also spam the jump button with the Duplicator, and hope that you get lucky and stay up for a sufficient amount of time. You need to spam at very high speeds(about 13-15 cps) in order to ensure you don't miss a jump.