If you're going for 100% completion, you've seen that 10000 headshots/kills are required. Unfortunately, these are glitchy and will often not count at all for anywhere from one 10 minute level to an entire 10 hour play session. I don't know the exact rules behind when they start glitching out, but I have developed a ritual that seems to get them to count 100% of the time for me.

1. Launch the game
2. Successfully play one level without tabbing out of the game (if I die, I close the game, but not sure if this is necessary)
3. Wait for the post level animations to fully play out, press Next once, then let the "We Are Thinking" loading screen time out instead of pressing Next again
4. Confirm I got headshot tracker progress in the map menu via steam overlay -- this shouldn't be necessary to actually get it to track, but is a nice check to make sure it's working
5. Close the game
6. Repeat

It's a massive pain, but it sure beats completing a 10 minute level or more and realizing you didn't get any credit.