Hero of Legend Achievement in Lightning Returns: Final Fantasy XIII

The description for these achievements is a little misleading as you need to win a total of 500 battles, not just defeat 500 total enemies. Boss battles count as well. This should come naturally as long as you do not avoid fights in the earlier chapters where the amount of enemies is low. After Day 9, enemies will begin spawning in larger groups so you'll fight fewer battles before they go extinct. There are always enough large-sized enemies that spawn alone available to still get to 500 battles, but knocking off minor enemies along the way is quicker in the long run.

This is also cumulative between all your NG+ runs, so if you don't have it after making multiple enemies extinct, you can always start a new playthrough in NG+ and continue working on it.