How to get the “But How?” achievement

Judging from other questions like this, it seems that SC2 keeps track of your progress in each mission separately from your campaign completion, saves, etc. So as long as you complete all required objectives for the achievement at some point, you should get it.

I believe you need to play through the entire game without shooting anyone to gain this achievement. If you mess up, you can reload your last checkpoint and go again but if you've passed another checkpoint since, you'll need to restart.

If you want to check as you go along, you can press the "Back" button and in the top-right of the screen it should say: "So far, you have not fired a shot at anyone". If you think you may have shot someone, hit the "Back" button and check this. If it's gone, you need to reload your last checkpoint. If it's there, you're good.

The bit with the convoy doesn't count as a shot and you can actually shoot guns in the game (at servers etc), as long as you don't shoot at anyone.