Staying off the ground means getting air time; performing parkour on top of buildings and zipping down power lines does not count. In order to unlock the trophy, you must travel a total of 130 meters or more in the air before touching the ground.
You can do this straight off the bat by climbing up the Cathedral in the main island. Locate the building which is on the west side of the island, then make your way up this giant obelisk. Once you're at the very top, take a deep breath, jump off, and use your Static Thrusters (+) and float your way down. Once you've hit the ground, breathe a sigh of relief, applaud yourself for attempting such a crazy feat and your trophy will unlock soon after.
You can also earn this trophy by jumping off the Ice Tower, which is actually a lot more daring but more fun.
(SPOILER FOR EVIL ENDING) An easy way to get this is to choose Kuo in the final decision for the evil ending and once John prompts you to press X to jump up you will begin to float around without touching the ground. Do a few laps around John's head and you will have this trophy.
You can also do this in the good ending ^^ , he just doesn't ask you to fly around.
The best way to do this while not on the last mission is to climb to the top of the ice tower and static thrust toward the longer street. (If I am not mistaken it is north). The top can already be blown off to do this.
The easy way to optain it: - use the editor and select an existing mission (the first is good) - stay on the road - press L1 that make you lift till you can. - exit the editor without saveing - you will be Cole on 200 mt in the sky, so press immediately R1 and fly for 130 mt