This Quest is unlocked when the following Criteria is met:
1) Discover 15 Areas using the Expedition Feature
2) Watch the skits related to the Expeditions
3) Unlock Terror Island aka Normin Island
4) Unlock the final Dungeon
When the Criteria is met, head to Yseult and visit the Inn. Speak to the Woman beside the Inkeeper to initiate the quest. She will mention a speaking Pengyon. You clearly want to see it for yourself, so sleep at the Inn and head out at night. The Pengyon will be on the beach not too far from the Inn. Speak to it and it will Transform into a man named Jude. Fight him and witness his Mystic Art for the "Witness to the Mystic" Achievement. He will mention that he is looking for someone and you will offer to keep an eye out.
Head to Taliesin and speak with a man near the Sanctuary. He will mention a Golden Pengyon in the Figahl Ice Caps. Head to where Rokurou, Magilou and Velvet crashed their ship after escaping Titania and you will find Milla. You will battle her and like the previous battle she has a Mystic art you must Witness for "Witness to the Mystic". Defeat her and they will walk off together and live Happily ever after...... Just kidding!
After beating the game. Head to Reneed and speak to the Katz on the long bridge. He will warn you if imminent doom on Normin Island and warn you not to go. Like all great listeners, you ignore that warning and head straight there. Go up to where the Normin Matching game is and you will battle both Milla and Jude. They will be around Level 126 and the world will be destroyed if you lose. No pressure. They also possess a Dual Mystic art you will need to see for "Witness the Mystic". Upon defeat you will unlock the achievement following a cut-scene.