Talk to the Girl from The Cure Quest to start with this quest. Located over Glastheim (P) (60,167)
She will tell you her sad story about her boyfriend. After that, you will be asked to find a Seer to help in getting an answer on her dream about her boyfriend.
Head to the middle part of the same map (around 200, 130) and enter the portal. Once inside, keep heading north passing by a priest named Morvas and into the stairs befind him. There is a portal just at the top of the stairs, enter it.
Once you enter the portal head over to the northern west part of the map to talk to the Seer (Located around 49, 126).
After talking to her, she'll need you to collect some items to continue. Upon returning with all the items she asked for, she will send you out to her friend who can open up a portal into the secret lair of the monster responsible for killing the girl's boyfriend.
Head to Hugel Field 02 and find the Conjurer (Located at 85, 211).
Once you are set up and ready, the Conjurer will warp you into the secret lair.
Defeat the guards and Malificent Daemon. (Donates are allowed as are Yggdrasil Berries.)
Once you've defeated all the monsters, you will be warped back and then you have to head back to the Girl.
She will tell you that her boyfriend's soul is at peace now and will give you the Skull Cap as a way of showing her gratitude.