This achievement is pretty self-explanatory, but just to be clear. In Anthem you collect loot and you are increasing your gear score. You need to have uncommon rarity of your Javelin, not your gear.
I completed a mission with uncommon items in all slots, but didn't get a cheevo, but then i increased my gearscore and it gave my Javelin uncommon rarity and after mission (it can be any mission except for Freeplay) it popped.