I've updated JumboWario's world to make this easier. Go into the back room. Here's the file (recently updated):https://www.dropbox.com/s/b8yt01cpkcpzycp/Achievements%20Imp...
His original world is in this forum: Minecraft World for All 1,000 Gamerscore
You have to do a little work, but it's pretty foolproof. Remember you don't have to make all of them, just have them. This is written so n00bs like me can do this from scratch. You can do this across multiple worlds (and I had to so I could get Brown).
Find the cave to the back and right of the spawn. Follow the rail a short way until you see a torch on top of a large cobblestone pile. The furnished cave is just below this on the other side.
Once there, make a new chest and put it down so you know what you have. (I also made a diamond sword and pickaxe while I was there.) From the ORGANICS box, take the Oxeye Daisy, Lilac and Cooked Chicken (for hunger). From the RESOURCES box, take the Lapis Lazuli. From the MISC box, take the Shears, the Cactus Green, the Minecart and the Bones. Take the White and Black Wool from the BLOCKS box.
In your inventory, put a Cactus Green on the left and the White Wool on the right. Take the GREEN Wool.
Take 2 Bones and craft them into 6 Bonemeal.
Repeat with Lilac to make 2 Magenta Dye.
Repeat with Oxeye Daisy to make Light Gray Dye.
Mix a Lapis Lazuli with a Bonemeal to make 2 Light Blue Dye.
Mix a Lapis Lazuli with a Cactus Green to make 2 Cyan Dye.
Mix a Cactus Green with a Bonemeal to make 2 Lime Dye.
Put everything but the Minecart, Shears and your sword and pickaxe (if you made them) into the new chest. If it's dark, sleep in a bed.
1-2. You now have GREEN and BLACK in the chest.
3. (You also have WHITE. It still counts even if it's not in the box. You'll know this works when you get to Brown.)
Go outside. Hop in the Minecart into the forest. After a bit, you'll see a rail off to the left. Get out of the cart and follow the rail. Pick up a bunch of Dandelions and Poppies when you see them. You need a few of each.
When you get to the town, shear all the sheep you see. You should now have plenty of wool.
Go into the house with the bed and shut the door for some peace.
4. Take all the Poppies and make them into Rose Red. Combine one with a White Wool to make RED Wool.
5. Take all the Dandelions and make them into Dandelion Yellow. Combine one with a White Wool to make YELLOW Wool.
6. Mix Rose Red and Dandelion Yellow to make Orange Dye. Combine with Wool to make ORANGE Wool.
Go back to the cave.
7. Use Magenta Dye to make MAGENTA Wool
8. Use Light Gray Dye to make LIGHT GRAY Wool.
9. Use Lime Dye to make LIME Wool.
10. Use Light Blue Dye to make LIGHT BLUE Wool.
11. Use Cyan Dye to make CYAN Wool.
12. Use Lapis Lazuli with White Wool to make BLUE Wool.
13. From your chest mix the Bonemeal with Rose Red to make 2 Pink Dye, and then PINK Wool.
14. Mix Rose Red with Lapis Lazuli to make Purple Dye, and then PURPLE Wool.
Now you have everything but GRAY and BROWN. Keep the sword, pickaxe, food, one Bonemeal and one White Wool. Put everything else either in your chest or another box (so they're safe).
You need an Ink Sac for Gray. Wait until day, then go into the ocean. Look for a squid and kill it. You should get an Ink Sac. Go to land.
15. Mix an Ink Sac and the Bonemeal to make Gray Dye, and then GRAY Wool.
You shouldn't have to put this back into the cave but you can. Quit to the title menu.
Start a new world. Under advanced, use seed 1405119578. This will spawn you between a jungle and mesa biome. Lots of cocoa beans hanging from trees. Get one, then go looking for a sheep. (Sheep are the hard part here.) Once you find one, kill it and take the wool.
16. Combine the Cocoa Beans with the White Wool to make BROWN Wool. The achievement should pop.
(Note: I spent a LONG TIME looking for a jungle biome in JumboWario's world but couldn't find it. This method worked for me, even across worlds.)
Until someone makes a new world, this is what worked for me. Most of the materials are really close. You just have to put them together.