Currently I want to hunt down all achievements. At this time it seems that achievements gets disabled if I start the game with a mod.
I would love to use info addict and Civ V Unofficial Patch (G&K), but I was not able to figure out how I can keep achievements enabled.
Get a list of all the achievements and of the ones you have done, then keep your own list without bothering with use-of-mod restrictions. Personally, being able to use mods is MUCH more important than the game achievements.
Of course, mods also disable the hall of fame. I keep a manual log of that too.