I am having a problem as well with the achievements. It's for the smoking corpses and get a grip. I have killed probably 300 units with kinetic blast yet it's stuck on 33, and I've used crushing grip on many units and it's also stuck on 93. This has been going on for a couple of days now.
So I beat the game, then looked at the portraits that I unlocked. It shows that I didn't get Kerrigan to level 70 and didn't give me the achievement or the portrait. The only problem is that I beat all the missions, got all the bonus levels, have Kerrigan at level 70, and I did all of this in the campaign and did nothing with the archives. I have no clue what the problem is and don't know if this is happening to everyone.
I just figured out the problem I was having with the Kerrigan objectives. They must be done within the same mission. So, for example, Leaping Death must be 15,000 damage that Kerrigan does during any given mission, including during Master Archive. I previously thought these cumulative over time, or maybe just in the course of campaign play. I am still not sure what is or is not triggering the level 70 achievement.
It's important to note for the Kerrigan achievements that your achievement list will tell you the best score you've done to date, but will not increase until you're actually past that marker while going for it in a mission.
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