This achievement requires you to have Purple level rarity (or higher) items equipped in all four weapon slots, and all four gear slots (Grenade, shield, relic, class mod).
If you are unsure, the rarity of items from least rare to most rare are as follows: White, Green, Blue, Purple, Orange. DLC for Borderlands 2 has added Seraph (Pink) and Pearlescent (Cyan) rarity levels. Pearlescent are ranked higher in rarity than Orange.
Eridium Tech weapons (Dark Pink text colour) count a purple and work towards this achievement (confirmed by Lavindathar - Thanks).
As obtaining purple level items is down to luck and how generous the game is feeling, there are few sure fire ways of getting these items to drop. What follows is a guide on how you can help speed up the process by looking in particular areas.
Guide may include spoilers by mentioning good bosses worth repeatedly killing for Purple level gear. These may be considered spoilers by some so be careful.
Purple level items in weapon crates on a regular basis but keep an eye out for Boss enemies. Bosses can be regularly farmed after they are killed in the story by returning to the area they are located in. Bosses like BNK-3R drop huge piles of loot which often include several purple levels items such as Weapons, Grenade mods and Class Mods. This also applies to The Warrior and Terramorphous The Invincible.
An Orange level shield can be obtained as a quest reward for completing the "Cult of The Firehawk" side quest line, which is given to you fairly early on after reaching Sanctuary.
A Purple level shield can be obtained as a quest reward for completing the the mission "This Is Only a Test' which is the final mission in the series of missions given to you by the residents of Highlands: Outlook
1. A Purple relic is regularly dropped by The Sherif of Lynchwood called 'The Sherif's Badge'. This should not be confused with the 'The Deputy's Badge' which you receive as a quest reward from the first time you kill her as part of a mission. The Sherif can be fought at the end of Lynchwood series of side quests which are available around the middle of the story. As with all bosses, she can be fought repeatedly by saving and quitting and then reloading the area. This will reset all the enemies, including bosses. Be sure to let her jump to the ground before you kill her, as reaching her loot will be difficult if she is still on the building she spawns on.
2. Durring the start of the story mission 'The Talon of God', there is a chance of Tannis gifting you a Purple level relic.
1. The Warrior is pretty generous in dropping purple level class mods, especially on True Vault Hunter Mode (Play through 2).
2. If you have the skill/equipment to kill him, Terramorphous The Invincible will drop a guaranteed Orange Level Class mod called "The Slayer of Terramorphous", however there is a 1-in-5 chance of it being for the Class you want.
Purple level weapons and shields have a small chance of being given to you by Michael Mamaril, an NPC that appears at random in Sanctuary (see the achievement 'Tribute to a Vault Hunter')
The Slot machines located in Moxxi's Bar in Sanctuary have a chance of dropping purple level weapons if you align three Marcus symbols, and a chance of dropping an orange weapon if you align three Vault/Borderlands symbols.
If you are truly desperate, purple level weapons can be recieved from the Golden Chest in Sanctuary, however this requires you to use Golden Key, and these can only be obtained through promotional codes, usually distributed via Gearbox's Twitter and Facebook accounts, usually at weekends.
These guys regularly post collected codes for all sources on this Facebook page, check it out regularly for updates:https://www.facebook.com/Borderlands2ShiftCodes?fref=nf
Pink level rarity was added with the Captain Scarlet DLC, and expanded upon with each subsequent story DLC. These are called 'Seraph' weapons and are dropped by the DLC raid bosses or purchased from a special vendor. I am unsure if these count toward the achievement, but they can be found for each gear slot except class mod.
'Pearlescent' weapons, which are in a cyan text colour are classed as rarer than orange, and only drop in the DLC from Loot Midgets and possibly the larger bosses.