The way you dye armor has changed. After you have collected the leather and made the armor piece(s) you need and collected the dye. Open the crafting menu
cycle the menu up and down.
cycle the menu left and right. Cycle down to the 4th menu. The first menu on this list changes the armor the second menu changes items. On the armor menu place the armor you want to dye in the first box and the color you want in the second. Do this with each piece of armor to unlock the achievement.
To dye your armor you will need 24 pieces of leather. Leather is found by killing cows. You will then need to use the crafting table craft a helmet, chest plate, pants and boots. Dye is found a number of ways. You can use cacti, flowers, coco beans, ink sacs, and a few other items. You will need 4 items of dye. Any combination of color or all the same color. To create the dye you need the crafting table. Dye is under the decorations tab on the crafting table. There it will show the items you need to make the color you want. Once you have all the armor items and the dye.
Open your inventory by pressing the . Then select your dye color by pressing . Move the item over your armor piece and then press . Do this for each armor piece and this should pop. Just know as of this writing the achievements aren't live yet.
This achievement should unlock now.
EDIT: as FinalKaos noted you only have a minimum of 8 pieces of leather and make one piece of armor and dye it, then reload your save.