Signature Arc Locations Maps
For all standard S-Class characters and some A-Class characters, NTE provide a free S-Class weapon you can get in-game, without any Gacha involved.
Most of these involve going to a certain location in open world, defeating a boss, and claiming the Arc. With one boss involving several steps tracking, and one hidden quest.
Signature Arc from Bosses:
Sakiri | 
Good Boy's Grand Adventure | Morphix
Baicang | 
Camellia Society | Serenetti
Haniel | 
Blow up the Crowd | Beat King
Daffodill | 
Youthful Fantasy | Black Tome
Fadia | 
Eternal Waltz | The Never-ending Arachne
Jiuyuan | 
Reality Refuge | Swallowtail
Hathor | 
Raging Flames | Headless Rider
Note that Hathor's signature Raging Flames require a bit of tracking of the Headless Rider, we have a dedicated guide to how to get it here.
Hidden Quest for Main Character Arc:
Zero's signature Arc 
Day Off requires a hidden quest that doesn't involve fighting, but takes a lot of travelling and setting the timer in-game. We have a full guide on how to get it here. The above Map shows the starting point of the quest.
Other S-Class Arcs from Bosses:
Some Arcs doesn't have an ideal user, and they are there as a stat stick, or a niche pick if a character has nothing else to use. These are:
Song of the Whale | Sea Prisoner
Tears Beneath the Mask | Nestbound Bird
Your Happiness is Priceless | No boss needed, just keep throwing coins in Nacupeda;s Pool daily until you accumulate enough currency to buy from the shop.