If you're like me, you got through the game without popping any of (or more bizarrely, only some of) the time achievements even though you've passed the allotted time/beaten the game.
I had the same issue and have periodically come back from time to time to give it another shot/see if it was patched, etc. On my most recent playthrough I think I accidentally figured out a trick to it.

I was going through and made it past 4am without any achievements again, when I stepped away for a minute to do some busy work while the game ran when - low and behold - the 4am achievement popped. Testing this out, I got the rest of the time achievements, as well.

TL;DR WHAT TO DO: Play the game (use a guide) and once you get yourself past each time barrier, STOP WATCHING VIDEOS. Just let it sit with the video business closed for a while. Believe it or not, after a minute or two, the cheevo should pop (it did for me.) I even played solitaire for a few of them.

This got me the full cheevo list after so many years of "trying," so hopefully it'll finally work it out for you, too.