Best way to kill the Ender Dragon in 1.9
Solution 1:
Besides, obviously, your best armor, sword, bow and arrows, golden apples and potions, you will need some building material to climb the towers, and some Ender Pearls. And don't forget a pickaxe to break Iron bars (and possibly dig End stone).
As before, you start the fight by shooting all the Ender Crystals you can, and after that you have to climb those pillars that have Iron bars around their crystals.
The fact that the dragon now regularly swoops down onto the portal makes it actually easier to predict its movements - it circles around the sky, periodically strafing the player with fireballs (a.k.a. "ender charges"), then lands on the portal, and then charges directly at the player. Both charges and strafes make it even more important to move, because a charge targets a position the player was some moments ago, and it is pretty hard to notice when a fireball has been launched at you.
After the crystals are gone, you can take your time and chip at dragon's health as long as your healing supplies last. Note that you can only damage the dragon with arrows while it is in flight - on top of the portal it reflects arrows back at you. After it lands, note the direction it's facing, run up to its side and start jumping and slicing it with your sword - you are safe as long as it is spewing acid in the other direction. After it stops, sprint away in a spiral, to dodge the charge.
Look for ways to minimize climbing by using Ender Pearls. Long-range teleporting can be very dangerous, as a missed shot can teleport you to almost the top of a pillar, and you'll drop and die. Be careful, or be prepared to throw a second pearl downwards to minimize damage. (Note that Ender Pearls have a cooldown of around one second in 1.9!)
Also, Ender Pearls can save you if a dragon does hit you with its wings and knock you high up in the air. Apart from substantial fall damage, it can straight knock you out off the island.