You can actually see a "Q" on the dungeon map as an indication of a current active quest you got in there, as well as in choosing the difficulty in a said dungeon it will also mark a "Q".
1 star = normal
2 star = hard
3 star = very hard
Left to right:
1) Clear 3-1 VH and 3-2 VH --> Skill Book Quest
2) <talk quest>
3) Clear 2-3 "Hard" under 20 mins
Left to right:
1) I clearly left this unfinished since its bugged from my part, most likely a PvP quest
2) Purchase "beginner scroll" (the cheap one) from Cammila(PvP).
3) Talk to mayor.
Left to right:
1) Get a weapon to +2 then talk to him.
2) Get 6 "Forgotten Time Fragments" inside Henrir's Time Construction (clearing until town 3 monsters then exiting will let you acquire this and you must have this quest recorded so that you can acquire the drop)