The game is still bugged in the 1.1 patch - better but not fixed. Achievements are no longer unobtainable but the game will degrade over time. Initially after install it'll work fine but after couple hours of playing power cycling the phone just before playing is required. After a few more hours the time to load just gets progressively longer. I'm now taking the approach of finishing a campaign mission and the associated collectibles achievement then doing an uninstall/reinstall. Uninstall/reinstall loses your current save and all museum progress (i.e. all progress towards achievements that haven't popped yet).
Antarctic is a multi-part mission. Find a diary, bring it to the farmer. Find the missing pages, bring them to the farmer. Find a crown, bring it to the farmer. Find another crown and resurface to end the mission.
Note that the objective after finding the 2nd crown is NOT to bring it to the farmer - it's to get out of the mines so as soon as you resurface (presumably with a teleport), the mission ends. So, if you want to finish Historian during the quest when you've already dug down 2000m, don't pick up the 2nd crown until you're ready.