Couple of things

[steverpg]

In the Mystic Woods going down the hole there is a rock that cannot break as it does not ask for AP. I have plenty, Also the guild says a monster is near the Temple of Memories and have searched all around it with no luck. Any comments welcomed, thanks.

[Euphoniac]

Breaking boulders is Evie's ability, who isn't present during your first visit in the Mystic's Woods. There will most likely be an opportunity to revisit this area later with your complete party (all the more so since one of the hunts takes place here).

At the Temple of Memories (outside area), talking to an NPC in the lower right corner should spawn the monster you're supposed to hunt (you can still prepare and save after spawning it, and then engage it whenever you want).