Question for the better runners: Is it possible to complete a heroic objective and get the achievement without finishing the mission? I want to figure out rule technicalities for All Heroics before they arise. It will almost certainly be a frustrating category.

Could just define it as finish each stage and achieve all heroics. I don't see how that could be exploited.

Yes, it is possible for most missions to complete the heroic without finishing the mission. But as long as we are not allowed to use Story Mode -> Continue for speedruns we have to beat the mission anyway to advance.
The only exploit I can imagine is a mission where it is faster to beat the mission, restart, get the heroic, exit to warrens as opposed to doing both in one go. Cannot think of any missions that fit this criteria though.

I've played it quite a bit on the standard map seeds and there still isn't really an option to abuse the fact that you don't have to complete the heroic as you finish the mission. Instead, it helps players keep pace if they got the heroic but couldn't beat the mission in that go.