Shining Resonance Refrain

After you finish the main story some level 100 enemies spawn around the world that you can defeat to unlock this achievement and new tunings. I fought all them around level 75 with little problems

Locations
Glaucus Falls
Fort Garhal in the boss/Church room
Gaelritz Prison on the roof
Gaelritz prision in the basement where you rescue Marion
Old Castle theater where you save Sonia
Logos Tundra Dragon shrine
Djimgharna Ruins Dragon shrine

"Powerful foes" will spawn in seven specific locations on the map during the post-game. These superbosses are not actually all that powerful with the exception of one encounter. The fights can be easily won by exploiting the elemental weakness of each superboss coupled with timely B.A.N.D. Sessions, and you should be able to defeat them all in the level 70s with little difficulty. My characters and Party were not even particularly well-optimized for each fight as I was leveling non-ideal Tunings at the time and had miscellaneous Aspects equipped (such as Millionaire and Steal Attack), but nonetheless you will see my Party crushes most of them even without Yuma using Dragonshift:

EDIT 8/23/2019: It came to my attention that the original Game Clips were removed at some point. I have since added new Game Clips; the main difference being that my Party is now level 100+, but the new Game Clips nonetheless demonstrate the efficacy of exploiting elemental weaknesses. A Party within the level 70s should still have relative ease with beating these superbosses (except for the Library of Memories fight), and as such the strategies remain unchanged:

1. Djingharna Ruins - Dragon Shrine: Level 100 Chaos Blood (weak to Light)


2. Glaucus Falls: Level 100 Urd (weak to Light) + Level 100 Skuld (weak to Wind) + Level 100 Verdandi (weak to Fire)


3. Fort Garahl - Maelgius Cathedral: Level 100 Vortec (weak to Water and Earth) + Level 90 Electron x4 (weak to Earth)


4. Logos Tundra - Dragon Shrine: Level 100 Hell Master (weak to Darkness) + Level 90 Hell Ghost (weak to Light) + Level 90 Hell Skeleton (weak to Light)


5. Mount Glanciel - Old Castle Theater: Level 100 Mad Bull (weak to Light and Darkness)


6. Gaelritz Prison - Top Floor: Level 100 Abyss Dragon (weak to Light)


7. Gaelritz Prison - Library of Memories: Level 100 Shadow Knight x7 [Musket Knight x2; Crossbow Knight x2; Grand Knight x1; Heavy Knight x2] (weak to ???)


The Shadow Knight x7 battle is definitely the most difficult of the superboss fights because they all hit absurdly hard, and can one-shot the lower defense characters such as Kirika with ease. Quite simply: The lower the Party's overall level, the more difficult this will be. I have not found a surefire strategy other than to abuse regenerative consumables such as Spirit Seedlings and Spirit Tonics from the Menu in order to keep the Party alive and thus gradually chip away at the enemies' health. These enemies also do not seem to have any elemental weaknesses. Killing the four ranged Shadow Knights should be the first priority because they also can inflict annoying status effects/debuffs on your Party members. Yuma's "Dragon Square" Force can knock-off a large chunk of the ranged Shadow Knights' HP, especially if they are grouped together.

Be advised that you cannot Escape from these encounters once initiated, thus if your Party wipes, you must either "Continue" until you defeat the superboss, or "Return to title."


Additionally, defeating a superboss for the first time rewards you with a Tuning for each character except Excella and Jinas. These seven Tunings are also required to complete: