A few key pieces of info: You need not kill every oversouled enemy, merely encounter them and have them oversoul to recieve credit. In fact, you will recieve this trophy mid-battle on the last fiend you need to oversoul.
Secondly, you need the non-oversoul entries for this trophy as well and again, a mere encounter is enough.
Thirdly, almost all entries can be done in the Via Infinito, but you must fight certain enemies outside it for them to appear there. You must fight Chocobo Eater in CH2, you must have failed at least one Heart of the Farplane puzzle to encounter Azi Dahaka (or you fight him in the Farplane Cup but that is very time consuming to unlock and unrelated to any achievements) and you need to defeat King VERMIN in CH5 in the Fiend Colony.
Two enemies wont appear in the Via Infinito at all. These are Georapella and Precepts Guard, found in that area in Bevelle you visited in Chapter 2 with the towers. You can return there in Chapter 5. Simply repeatedly interact with the towers to encounter them over and over to oversoul them.
With this in mind, be smart. Every 3-4 floors on the Via will have the same group of enemy formations. Get a species to oversoul and then DON'T kill them, merely escape from them in battle and you can save that oversoul state for the next member of the species you encounter deeper in the Via Infinito. See some new formation? Make sure you get every oversoul from every formation found on that floor and escape. Continue deeper until you find new formations. Rinse and repeat.
Many have trouble encountering Oversouled Mega Tonberry without dying given that you can't escape from him. If you're too weak to beat him legitimately I recommend trying a cheeky Bribe or CONGRATS! from the Random Reels in the Lady Luck Dressphere. You will probably die but you'll eventually get away. Elder Drake can be encountered in an escapable encounter on floors 80+.