To Spawn the wither, simply place 3 wither skeletons on top of 4 blocks of soul sand. Be sure to have the difficulty NOT set to peaceful. Use this world to make things easier. If you want to go for this by yourself, you will need to get soul sand in the nether, and wither skeleton skulls from the nether as well (by killing wither skeletons).
Killing the wither is slightly more difficult. Is is obviously easiest on easy difficulty. You will need to keep slaying the wither with preferably a diamond sword. Keep eating golden apples when low on health. When the wither is out of your swords' reach either use bow+arrow or try to get close enough to the wither.
When the wither is at 50% health he will spawn a few wither skeletons. It is then much more easier to kill him, as we won't fly that much/ that high anymore.
If you're unsure how to get the worlds onto your PC/android/ios device, the following forum I started might help, otherwise there are plenty of youtube videos.Achievement worlds
You can download the Wither world from here:
Edit: I've added SeanGamerPro's world, which has all 0.16 achievements in there.
0.16.0_Achievements_World It's much easier to kill the wither in here.https://www.dropbox.com/sh/v6ggssr1ag7uerp/AACU3QfRen68hOMno...