Sub Quests - Post Game
These side missions become available after you complete the story. And while there are only a few of them, two of the four quests will require quite a bit of work to complete.
Another Hillside Anomaly
The mission unlocks in Viscint post-game and after you've completed the sub-quest Spirit Temple. The client asks that you take care of whatever's got his cows spooked. Head to the Tietal Plains and enter Earth Spirit Temple. At the center, where Grand Gnome once was is a Renan researcher. Talk to him and he'll give you the Destiny Key. That concludes this quest.
Otherwordly Visitors
This one starts immediately after you complete the previous quest. The man asks that you retrieve six keys from beyond the gate to help with his research. He will then give you the Destiny Key which unlocks the first area of the dungeon.
Take note that this mission involves clearing six different areas of a high level dungeon, with enemy levels ranging from 60 to 95. Some areas also have cameo boss encounters against characters from previous Tales games. Check this page for more info.
Record Collection
There appears to be conflicting accounts as to how this quest actually unlocks. But here's what I had: bond with Dohalim is maxed; 21/23 Artifacts and no Realm Unifier for Alphen. However, I did not have any pending sub-quests in Viscint either.
Anyway, you'll find the Wonder Bard outside the Training Grounds in Viscint. Talk to him and he'll give you device to supposedly record people's voices with. Travel to all five realms and speak to every key NPC you encountered throughout the game. The people you must chat with are marked on the map so you won't have any trouble finding them.
The Reminiscence Device
The client for this mission is at the Lower Level of Daeq Faezol. He wants you test a device that allows you to fight enemies you've previously beaten. In other words, this is a high-level boss gauntlet challenge.
For starters, you'll have to defeat each of the five lords individually, then fight all five of them together. The final encounter will be against Phantom Zephyr who happens to be a level 100 enemy.