Just like the challenge says, complete all missions in Operation A with the Black Eye Skull active. This means that you have to melee enemies to get your shield back. However, you can also use Regen Field as your armor ability to regenerate your shield. That makes this challenge much easier than it initially appears, especially on mission 5. In some missions you don't actually start with Regen Field, but it is available for pick up during the mission. For instance, on mission 5 there is a Regen Field pick-up just above and to the right of the main platform. Hope this helps someone out.