These sets will be collected as you go through the game and open every chest. Some of the sets are separated in different chests and areas so you have to look everywhere. The starting set for your class is also included in the tally. Below is what I had on me when the achievement popped. I've listed the locations for some of the items, the ones I can remember anyways. Will update as I am able.
*Edit - I added the Lords (Heavy) and the Effect (Medium) armor sets to the list.*
HeavyWarrior - Depends on starting class; can also be found in chests either in starting Citadel or in Monastery.
Fallen – Chamber of Lies; 3 different chests
Eternal Legend – Wrist/Leg in small western antechamber of Temple;
Will -
Living Legend – 2 different chests in the Catacombs; Head/Leg/Chest in one.
Griffin – Abandoned Temple; 3 different chests as you make your way to the Infiltrator.
Symmetry -
Lords - 1 chest in final Proving Ground after defeating the brothers.
MediumCleric – Depends on starting class; can also be found in chests either in starting Citadel or in Monastery.
Faith -
Wisdom – Head/Chest in East antechamber of Temple;
Live Elements – 2nd tower of the Monastery in multiple chests.
Harmony – Catacombs; all in 1 chest.
Blessing -
Effect - each piece given while
LightRogue - Depends on starting class; can also be found in chests either in starting Citadel or in Monastery.
Cold Blood – Catacombs; 3 different chests.
Hot Blood – Head/Chest in 1st tower of ramparts of Monastery; Leg/Wrist in 2nd tower.
Cunning -
Dimensions – Planetarium; all in 1 chest.
Persistence – Head is in the Beast Cage;
Demon Assassin – Located in Chamber of Lies; 3 different chests.
I also had 2 of 4 pieces of the Last Traitor (Medium) set you get by using Tor (Great Hammer found in Chamber of Lies on the floor) on the statues in the Rhogar realm. I suspect this will also count as one of your sets if you manage to get it before completing one of the others.