You cannot get a complete list of enemies until you finish all 3 paths. I do not know if you need to do this using clear data (which means 3 complete playthroughs). However, your save file shows 1 * if you have cleared once, and 2 * if you have cleared twice. [Note: even after 3 playthroughs from the very start, I’m still missing two low number enemies.]
You start a replay at level 1, but with all your equipment and souls. So you are more than strong enough to auto through every battle even at low levels, and can defeat all the bosses without any additional grinding. This means it is not necessary to grind to high levels (40 max is all you should need).
Also, don’t bother with the Hourglass of Memory. I was hoping to use it to repeatedly battle the “special monsters,” but alas it seems that they appear only once per playthrough.