Rainbow Collection - Gather all 16 colors of wool. - 20G
This one is going to be long run for you. You need to collect all 16 color dyes in the game. Some are easy to obtain, some aren't. I'll list them all down below.
Bone Meal - Made from one bone. Easy to get, kill a skeleton, go to crafting table and craft. I'd suggest getting a few of these.
Ink Sac - Killing Squids will always obtain this, killing one squid will drop between 1 to 3, you can also get 10 at once as a "junk" item while fishing, collect a few of these.
Gray Dye - This is only obtainable by going to the crafting table and having one Bone Meal and one Ink Sac, going to the crafting table and crafting it, it'll let you get two Grey Dyes
Light Gray Dye - This is only obtainable by going to the crafting table and having either - One Ink Sac and Two Bone Meal , Or - One Grey Dye and One Bone Meal.
Rose Red - Find a Rose, go to the crafting table and craft Rose Red Dye, it'll give you two of these. If you can't find any Roses, first, wow. Secondly, grab one bonemeal, and use
on some grass, this'll spawn some grass, Dandelions and Roses.
Dandelion Yellow - Grab a Dandelion and go to the Crafting Table and craft Dandelion Yellow, if you can't find any Dandelions, grab one bonemeal, and use
on some grass, this'll spawn some grass, Dandelions and Roses.
Orange Dye - Only Craftable with one Rose Red and one Dandelion Yellow.
Cactus Green - Find some Cactus, they are usually on Sand. Go to a furnace and smelt it. The fuel you use to smelt doesn't matter. You will get one Cactus Green. Be sure to make two.
Lime Dye - Only Craftable by having one Bone Meal and one Cactus Green.
Lapis Lazuli - To obtain Lapis Lazuli, you need to go mining, this Ore seems to be the second rarest ore to spawn for me. I can't really help with finding it as minecraft randomly generates worlds. Breaking the ore will drop a lot of Lapis Lazuli. You better hope it dropped at least Five. We will need the other four for four other dyes.
Light Blue Dye - You will need one Lapis Lazuli and One Bone Meal
Cyan Dye - You will need one Lapis Lazuli and one Cactus Green.
Purple Dye - You will need one Lapis Lazuli and one Rose Red
Pink Dye - You will need one Rose Red and one Bone Meal
Magenta Dye - There is three ways to make this Dye
1. Purple Dye + Pink Dye
2. Lapis Lazuli + Bone Meal + 2 Rose Red
3. Pink Dye + Rose Red + Lapis Lazuli
I suggest the third method.
Cocoa Beans - Luckily the 360 version has Jungles. Head to a jungle and you will see some orange pods hanging from Trees, destroys these for an sum amount of Cocoa Beans.
Now, to get wool, you need to find sheep of the white colour, craft a Shear and go up to the sheep and shear them, this gives around 1-3 wool, rather than the regular 1 from killing a sheep. Collect 16.
Head into the crafting table and craft all the wool you need for each dye. Achievement Unlocked!