Board Countermeasures can be started through Control Points. They are short objective missions with requirements to kill certain enemies in different locations or use a certain weapon forms/abilities to get kills etc.
You can select 3 at a time, so this shouldn't take too long. I would recommend choosing an objective which doesn't mean you have to go out of your way, i.e. if you're doing some missions in the Research sector, get a countermeasure that involves getting kills in this sector. You can hold
to get rid of a countermeasure from the list once you've accepted it, so to make it easier you can just keep getting rid of them till you get some easy ones. My favorite easy ones were the weapon form specific ones, or ones for using Launch.