Legendary sets consist of six armor pieces: helmet, chest piece, legs, shoulders, gloves, and boots. All pieces of a set must be equipped at the same time for achievement progress to be made. Progress is account wide and not tied to a single character.
There are eight sets available in game. Unsure if the Ancient Ember set counts toward the achievement.
Four sets are class specific.
Musketeer Garb - Sharpshooter
Cosmic Garb - Railmaster
Celestial Garb - Dusk-mage
Mountain King's Garb - Forged
Three sets are region specific.
Woodsbeast Garb - Goblin
Skittering Garb - Hyvid
Arc-Powered - Voltura
Finally, one set, the Ancient Ember set, drops in Fazeer's Dun'djinn
It is unlikely you will acquire a full class set prior to reaching level sixty with a character. Grinding levels in Fazeer's Dun'djinn (the end game) that give the +50% gear luck modifier will be your best bet in polishing off any missing items. Region sets will drop in the respective levels in Fazeer's Dun'djinn. The chest pieces for each region set give a +20% gear bonus for a brief time after killing the monster associated with the region which is a boon when finishing off the region, or class, sets. Finally, all of the class and region sets can be acquired through the gambler and legendary gear bundles given through contract completion.
If you have any additional tips or corrects send me a message.