Go to mercenaries guild after talking with Otto go to second floor to talk with Zoey (Just go down he is on the end of the room). Before you go out buy new equipment in shop. Now go to Tarim Wood and keep going north until you see a board signand go to …rim…. direction
Tarim Cave
Careful!! In gray colored area you will fall if you walk near it.
No boss battle in this dungeon. Just back to the town after you finished the quest.
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Also, you missed out mentioning a treasure chest.
It’s just on the north side of the gray area.
The chest contains a Panacea Medicine.
one edit to your map, it’s stone of earth 2, instead of just stone of earth.