Just for those of high enough level, I did an AC dungeon run in story mode a couple of days ago as a lvl80 character and the reward was 177k XP. I guess around lvl70’ish should give you enough for the achievement so if you are high level and need it try a dungeon.
PS. Not sure if that’s the standard reward or being my first ever dungeon run had something to do with it but it was all a single reward, excluding the mob kill XP I got earlier, so you can die freely – as I did=D