Here is the full list of all 18 Quick Quest achievements.
Beaten the buffalo
Beaten the reptile
Beaten the varan
Beaten the salamander
Beaten the squid
Beaten the goat
Beaten the steel knight
Beaten the mask
Beaten the smoke knight
Beaten the cerberian
Beaten the lady knight
Beaten the knight of darkness
Killed 100 enemies
Killed 150 enemies
Got 9 Life Points
Dragon VS Dragon
Run Complete in Normal difficulty
Run Complete in Hard difficulty