I'm recent 5x80 with my toons, so haven't had any high-end epic moments. But I loved '1-shotting' trash while leveling. I especially enjoyed doing every Group quest without asking for assistance from friends/guild. Along with that, enjoyed killing the 'boss'/objective so fast that the NPC's special abilities weren't used. Those are the non-achievement-Achievement moments.

On a side note, doing the Hodir dailies where you feed the ghost-giant a worm... I have to melee cause my team casting will blow the mobs up before triggering the objective... I doubt that single players have that problem.