Since there is no guide for this achievement and Unifying Force I figured that listing the relationship levels and how to raise them would come in handy for newcomers to the game.
Friendship level can be raised by talking with the characters after a mission (every single mission), taking them out to missions with you, and completing their quests.
The friendship levels are: (Credit goes to Fear2424 at GameFAQs)
Acquaintance
Companion
Confidant
Friend
Trusting Friend
Devoted Friend
Kindred Spirit - I have found it that at this point you will be able to have randomized encounters with characters at the Pool of Purity. Make sure you don’t invite anybody to the Pool of Purity in order to spawn a random character in it. Also, please note that you might be kicked out of the pool by the character inside (which will reduce your friendship level with that character) or you will be allowed to stay (which will increase the level). So, make sure you save BEFORE going in the Pool of Purity.
Unbreakable Bonds
Soulmate - At this point, you will be allowed to invite the character to the Pool of Purity.
True Soulmate
Ultimate Soulmate – Trophy will unlock right away if it doesn’t just go inside the Slayers HQ or your home as it seems to unlock after loading.