Adding to Hakuro's list:

'Old Maid' achievement is from the FATE 'Poor Maid's Mishap' at Poor Maid's Mill in Upper La Noscea (a coruel whose name I can't remember at the moment)
'Lazytown' achievement is from the FATE 'Lazy for You' at Nine Ivies in East Shroud (against the giant ochu NM Lazy Laurence)
'Reign of Fire' achievement is from the FATE 'Svara's Fall' at Steel Vigil in Coerthas (against the dragon NM Svara - I'm not sure if you have to do the first two Svara FATEs 'Svara's Fear' and 'Svara's Flight' though to get the achievement)