As @DBC said, and I said earlier, the Missions unlock in order.
You have to complete one before the counter starts for the next. Any enemies of that type you killed before the Mission unlocked don’t count, no matter how many you’ve killed.
And the Missions don’t all unlock at once. Some arrived when Season 2 was released, and the others unlock as you complete Missions before them.
If you go kill some Undead Privateers right now, you should see your counter start to increase.
If you do that now, and don’t see your counter increase at all, then you can contact Support:
But it definitely will NOT count Undead Privateers you killed before finishing the Mission before this one.