You begin to unlock Heroic (purple) armor when you reach Level 3 Reputation (or 3rd prestige, if you will).
Once you hit Level 3 Reputation (and have a plentiful supply of Steel to spend) equip as many pieces of Rare (blue) gear you have. Go to Scavenge Gear and begin buying Premium Packs. Premium Packs will give you 2 pieces of gear that are higher than your currently equipped piece of gear for that slot, guaranteed.
I would suggest only buying about 3 or 4 of the Premium Packs because they are expensive. Keep track of which slots for your character you have and haven't gotten Heroic gear for already.
If after opening a couple Premium Packs you are missing a:
-Heroic piece for your weapon: start opening Weapon Packs (gives you 1 piece of weapon gear higher than your currently equipped piece of weapon gear for that slot, guaranteed)
-Heroic piece for your armor: keep opening Premium Packs (personally I think, since there are more armor slots to unlock gear for, having 2 chances at better armor gear is better than 1 with an Armor Pack)
(Note: Purchasing the Weapon Packs are cheaper and will increase the chances of you unlocking a Heroic piece of weapon gear for a specified slot you need versus getting armor/weapon gear duplicates from Premium Packs.)
Now, to actually unlock the achievement you must equip a Heroic piece of gear in each slot and then back out to the initial Characters/Loadouts screen. It should pop for you then!