I've made a new set up for this, got it on the first try on a dummy account. Download the Super Sonic Easy world (Windows 10 one for windows 10 version, regular one for Pocket editions), from the link above. You already have the elytra equipped, just walk forward towards the sign that say SUPER SONIC with an arrow pointing downwards. Make sure not to go too far to the right (open area). Once you see the ground getting close (Obsidian blocks + torches should make it easily visible), press the jump button to use the elytra. Only thing how you can fail this is by moving to the the right, which will make you land on the obsidian block. I've not placed blocks here to allow yourself to have an indication of when to use the elytra. Solution for SUPERWERELD (Old solution)
In this world, kill the ender dragon, then take the teleporter, and press skip to skip the credits. This will take you back to the main world. Then, head over to the area in the back where it says update 1.0. In there, go to the back right. There is a large pile of dirt coming from the ridge. Retrieve a piece of elytra from the chest below, and use the ladder. Also make sure to equip the elytra. Don't go all the way up, but instead go to the right about halfway up the ladder. Then look to your right, and you can guess it, you will need to try to fly through one of these holes. I suggest making a save at this point, which you can reload if you fail and die. (it's faster than running back, equipping the elytra again and going up the ladder).
I found this easiest in 3d mode, go to settings, video, then change to third person. You will need to jump/ run of the platform, then you will fall down, press the jump button again, to use the elytra/cape. You will either die by landing on the dirt, or unlock the achievement by landing in the water.