EDIT: with the new updates, the tutorial world has changed. I will always recommend doing this achievement in a tutorial world because the developer makes sure all of the elements are present to complete it are present and there are usually easily found stockpiles of materials laying around.
Sorry for the wall of text, but my capture device is bugging out.
I started a new world and planned on using it for all of the new achievements. After spending a good amount of time and getting a good deal of achievements I used the same seed to make a copy world that I was able to be in creative. I actually wound up with a world without a portal and was greatly devastated. Luckily the tutorial world has a portal and a lot of resources ready to use in all the right places.
The hardest part of this is actually getting to the dragon, so this will also focus on entering the end. Play The Tutorial Level on Easy to start. If you want, you could technically start on Peaceful, but you will need to kill some mobs to get some required items. This took me the better part of one day to do, but I was not playing my best. Realistically, it might take a couple of hours. Save often, especially prior to tense situations like the nether and disable auto saving when in the nether just in case.
Skip as much as you can with the tutorial. After second playthrough, I set my controller down and waited for it to say press
to skip. The first time, I got sucked into the Zelda owl trap and kept mashing
when I should have been paying more attention to the text box because it wouldn't allow me to progress. Once you leave the initial area head over to the enchantment area and check the chest for the Bottle o' Enchantments and blaze powder. The bottle o' enchantments will help you power level and get the point where you can enchant a very nice sword that will speed things up. Next, head on over to the area with the anvil and there should be another 64 Bottles o' Enchantments, an enchanted shovel, and an enchanted stone pick axe. Right next to this is the beacon and a chest. Check the chest for some iron ingots. Use these ingots to craft an iron pick axe.
After you have secured all of these items head in the direction of the castle and behind the villager that trades for paper, there is a shore between the village and the castle . Down there is a chest full of boats. Grab the boats and place one in the water. Following your map head to the coordinates: X: -211 Y: 83 Z: 331. As you near these coordinates you will see a large pirate ship, next to a mansion. Climb up the ladder and head into the mansion. Once inside, the first door on your right will be the inspiration room. Go to the left and in the corner will be two blocks of diamonds. Head back into the main hall and directly across is the kitchen. There is a good amount of food here that you can take.Head back to the main hall and continue inside to the next micro hall that leads to the stairs. You can take either side down and you will go down two sets of stairs where there will be a room on the right labeled "Library". Once inside there is a fireplace with a lever on the left. Flip the switch and that will open a secret passage in the fireplace that leads to another block of diamond. (I managed to do this with just the two from the "inspiration room").
After you have acquired The diamond blocks head back upstairs to the main hallway and continue inside. You will pass the glass area and there will be a sign indicating "store room." Grab the bow from the chest on the left hand side of the room marked "tools weapons." Climb up to the next floor where there is a large painting on the wall with a pressure plate in front of it. Before heading inside, if you haven't already use one of the crafting tables near the brewing stations to craft at least one diamond sword. Head inside the hidden door behind the painting and you will find an enchantment table.
SAVE!! Enchant your diamond sword to specifically get the loot attribute. You will want this as you will have to acquire several (in my case 9) eyes of ender (Ender Pearls + Blaze Powder). If you are going for other achievements (like Zombie Doctor) this mansion has a lot of items that help. Before leaving the area, check the dispensers on the pirate ship for arrows. I took way more than i needed. A row should be more than enough. I think I went through 1 and a half stacks fighting the dragon and taking out the crystals.
Now you have some farming to do. You can either hunt the endermen first or go after the blaze rods. For the blaze rods there is a nether portal located in the starting village inside the basement of that giant castle Coordinates X: 95 Y 62 Z: -92.
SAVE!!! You enter the nether at X 35 Y 55 Z -29. Head to the coordinates X: 122, Y: 62, Z: 107 to find a blaze spawner. Each blaze rod is good for 2 blaze powders, so I'd recommend getting at least 5 and they are not guaranteed. I dug my way through a mountain and then up inside of the nether fortress. It was quite a journey to get to the blaze with lots of gasts and wither skeletons trying to prevent my success.
For farming the endermen, there is a really nice flat desert land to the east of the mansion at X: 155 Y: 56 Z: 256. This is also extremely close to where you have to dig down to get to the end portal. I was also able to acquire a good amount of XP from other mobs that spawned and where I found my zombie villager for the Zombie Doctor achievement. Hopefully you get lucky with the enderman and they actually drop ender pearls and spawn consistently. After you mix the blaze powder with the ender pearls to make 10 or so eyes of ender you should have enough experience to enchant a bow to get some decent added damage. The bow I was using had Power IV, Punch II, & Flame I and did way more damage than my sword. Craft the remaining diamond you have into armor and head to the coordinates X: 41 Y: 35 Z: 218 to find the ender portal. I had to eliminate some water from the dig site, but after that I was clear to just dig straight down.
SAVE!! and be careful as the portal is dangerously close to a ravine that has a good amount of lava as well.
From here save and quit out. Switch to peaceful and enter the end. If you do not switch to peaceful, you will have an unlimited number of angry endermen attacking you the entire time. Climb up the mountain and start taking out the crystals atop the large pillars. I used sand to climb up to the top of the pillars with crystals behind the iron bars and used my pick axe to get to them. I shot the Remaining crystals from a distance to cut down on the time. Once all of the crystals are destroyed the dragon will not regen health. Wait for him to swoop down and line up your shot and fire away. He will spew some toxins at you from time to time, but with diamond armor and the peaceful handicap you should be fine, if you side step out of the way. A few minutes of shooting him and he will go down without a problem.