How do I get a Critical Hit?

I found references to Critical hits here, but it doesn't really answer the question fully. I recently had an objective to get 5 critical hits, but I wasn't sure if that had to be done during quests. I've had several raids of raiders and molerats, but it remained at 0/5 all though this. I've done the Red Rocket quest, along with a few others, and it still remained 0/5. What exactly has to happen for this objective counter to increase? Is it a manual action I have to take during combat, or does it happen automatically?

Edit: Added screenshot of Objectives panel.

When your characters are on quests or you are prompted with the opportunity to explore a building with a dweller exploring the wastelands, you will go into a "combat view".

In this view, you can order a squad of up to three people (only one for the exploring dweller) and order them to go from room to room. They will face enemies and battle them, similar to how you are used to, except you can now micromanage which character attacks which enemy. After some time, based on your character's stats, a crosshair will appear over one of the enemies, if they don't die first. This icon means that one of the dwellers attacking the enemy has built up their critical bar.

Once you click on the crosshair your dweller will perform a critical hit, during this time is paused for the rest. You are expected to tap a symbol when the indicator is in the center leading to (?) 5x regular damage. How fast this indicator travels depends on your dweller's agility. When you land it badly, your free hit gets a significantly lower multiplier.

You do need an overseer office to start quests, and then send dwellers on quests. Alternatively, have many dwellers explore the wastelands and keep an eye out for a map icon in the top left.

Since this question wasn't fully answered yet, and for the sake of those who might still be looking for an answer to it like I was, I just discovered that you have to finish the quest and make your way all the way back to your vault before you get credit for any perfect critical hits you made while on a quest.