Epic-Level items are items with there names colored purple. There are 2 ways to get an epic level item, First, Loot a rare mount, Second, Loot it in a Dungeon.
Lets start with the first since this is the way i did it.
When a rare mount spawns it is announced in the chat box to everyone online as well as the region that it is in. Finding it from there isn't too tricky since Rare Mounts will only spawn in PvP Zones.
To capture mounts you need Bind Stones which have a 5% chance of catching a trappable mount, These can be bought in Greenmount for 5g each or 20g for a box of 5.
I recommend bringing 30+ with you when you attempt to catch one as the chance of catching is so low. Once the bind stone catches the mount you can then run up and loot the Epic Mount's Bond for your achievement.
Now the second way, Dungeons are a big part of Order & Chaos, Especially at level 60. At level 60 you Receive daily quests to complete dungeons on Legendary mode, This makes it easier to find a group since all the level 60s want to do dailys in order to get the best gear. Find a group, Pick your dungeon and hope for an epic item. Your chances of getting an epic item off of one of the bosses in a dungeon are pretty good when your on legendary mode. Now heres the important part, when the epic item drops you'll have the option to roll for it or pass. Do Neither. Instead loot the enemy that dropped it and attempt to pick up the Epic item. Whether you actually pick it up or not doesn't matter, As long as you clicked on it your achievement will pop.
You will not get this achievement from Crafting/Trading/Buying Epic items.