This achievement requires you to recruit all 9 possible companions in a single playtrough. Not too difficult, i got this without really trying and without using my Inquisitor perks to unlock dialogue options.
Most of the related quests unlock during normal story progression. I had all companions and the achievement unlocked on arrival at
A few need to be hunted down although with the possible exception of Sera they are easily found. Once you have met them, talk to them whenever you can and after a while you will get the option to ask them to join the Inquisition.
The Companions are
*** Spoiler - click to reveal ***Blackwall (Quest "The Lone Warden" in the Hinterlands.)
Cassandra (Met at the start of the game. Your first companion)
Cole (Quest "Champions of the Just" or after the battle of Haven)
Dorian (Quest "In hushed whispers" or before battle of Haven)
Iron Bull (you will get an invite to meet him after Val Royeaux. He is in the Storm Coast)
Sera (Quest "A friend of Red Jennys")
Solas (You will meet him at the first fade rift with Varric)
Varric (At the first fade rift with Solas)
Vivienne (Quest "The Imperial Enchanter")