I have come across a way of making this achievement relatively easy to get, cheese and all.
Once you progress the story far enough you can create your own Priority Assignment by interacting with Astropath Remigius Klemet (NPC standing to the right of the starmap). The power level of the assignment created is relative to your currently equipped power level.
Note: I was at power level 500 when I did this.
First, I unequipped the majority of my gear until I was power level 100. I then interacted with the Astropath and created a random assignment at Impossible Difficulty (This adds +250 power to the assignment). An assignment of 350 power was then created, I then re equiped my gear back to 500 and then sailed through the 4 missions to complete the assignment and pop the achievement.
The power level of the assignment went up to 420 on the last mission FYI ... so bear in mind the increase of difficulty as the assignment progresses.
This method can also be used to unlock the other achievements relating to Priority Assignments if you felt the need: