Could some new dungeons have bonus objectives?

[Morningstar1337]

As for why these optional bosses show up, I have an idea.

After a point in the story, various horrid beasts and fell creatures wound up twixt between the Lifesteam and the Void, placing them in different time frames, be it past, present or future, as the only people (canonically: person) that could potentially time travel, you are tasked with defeating these mobs to preserve the timeline. Instead of just being unable to change events of the past, the WoL must prevent other time travelers form doing the same.

As such these monsters are given either "Chono" or "Time Displaced" additions to their names. The quest where this happens can even be a Chrono Cross/Trigger refernce