You can get this achievement and "You Need a Mint" if you bring along some glass bottles in addition to your needed supplies to collect the Dragon's Breath. If you follow this guide and do that then you'll have:
You will need 16 Eyes of Ender, which are crafted from ender pearls and blaze powder. In the Elytra tutorial world, the end portal is empty. All 12 blocks need Eyes of Ender for the portal to work. The extra 4 are for the End crystals.
Getting Ender Pearls:
There are Cleric villagers, the purple-robed ones, in the village at x=107, y=81, z=-215.
Mine out a few of the gold blocks on the tall towers near the Elytra. These have a high value when traded to the villagers. Also, mine out some emerald blocks. Make these into gold ingots and emeralds respectively. Emeralds are needed to purchase the Ender Pearls.
When you give a cleric villager enough gold or trade with them enough they will take on a green sparkling effect. If you do this enough, they'll have Ender Pearls. If they run out of ender pearls, just trade them more gold. Do this until you have at least 16 Ender Pearls. You can also get ender pearls by killing Endermen.
They're found in the Aquatic Update tutorial as well.
4 Ghast Tears are found in the brewing area of the tutorial. This is all you need.
Getting Blaze Powder:
10 blaze powder piles can be found in the brewing area of the tutorial. You will need at least 6 more. 2 piles of Blaze powder can be made from 1 Blaze rod. Blaze rods are obtained by killing Blazes in the Nether. An activated Nether Portal can be found at x=132, y=50, z=-119. Actually, you can just go out and come back to a freshly stocked chest full of them.
Thank you for the great guide! However, you don't need to go through the trouble of killing blazes for more blaze powder. There is a feature in the tutorial world where if you take items from a chest then go to a different area, they will respawn in the chest. Instead of killing more blazes, I just went to the farming section of the tutorial and came right back and there was 10 more blaze powder waiting for me in the chest!
You need 28 glass blocks. Glass is made by smelting sand in a Furnace. You will need to gather 28 sand blocks from beaches, deserts, or other places. Then you must smelt them in a Furnace. If you can obtain a bucket of lava, use it. Using this type of fuel will net you this achievement if it's your first time doing so:
This fuel lasts for a very long amount of time, so you don't have to waste wood blocks, planks, or other burnable supplies.
An End Crystal is made from 7 blocks of glass, 1 Ghast Tear, and 1 Eye of Ender. You will need 4.
Fighting and Respawning the Ender Dragon:
Note: Make sure you save before entering the End Portal so that you can reset the End if you can't destroy the End Crystals. If you entered the End, can't destroy the End Crystals and can't go back, you can still reset the End. Doing so will teleport you with all your supplies back to the main tutorial area.
An End Portal is found at x=172, y=30, z=117. Place 12 Eyes of Ender in the holes of the blocks to activate the portal and enter. You'll have to dig you're way up out of a room at first. Now for the Ender Dragon fight. Use stacks of blocks such as dirt or stone to climb to each tower. Make sure you avoid the purple balls or expulsions of Dragon's Breath the dragon sends at you, as they can damage you. You can also collect the Dragon's Breath in glass bottles. Make sure you stand at the edge of the pools of the substance so you don't get damaged. When you destroy an End Crystal, the resulting explosion will push you. A good technique is to jump on top of an End Crystal before you destroy it since this will send you upwards and prevent you from falling off the tower. Another technique is to run towards the End Crystal while destroying it to counteract the explosive force. You can also place blocks around the tower tops, around the whole square or just in the direction you're pushed to prevent you from falling if you have time. It takes some practice with timing and technique to get it right. Once you get used to it, you'll be able to consistently do it. Save after each crystal is destroyed in case of any mistakes. Once you destroy all of the End Crystals, the dragon can't heal anymore. Every once in a while it will hover near the central square of bedrock. You can use your sword to hit it. If you have a bow and some arrows, you can hit it at other locations as well.
Neptune Diamond says:
In the new aquatic update the portal is at x = 25 Y= 9 and z = 30.
In front of the huge creeper statue, just dig straight down.
Once you kill the Ender Dragon, place an End Crystal on the central block of each of the four sides of the portal. These will automatically restore all destroyed End Crystals and respawn the Ender Dragon, netting you this achievement:
Trainerx says: You can also use snowballs to take down end crystals. The higher ones are a bit harder to hit, but snowballs are a lot easier to get a lot of than arrows.