This is 1 of the 4 Achievements (Empire, Warzone, Fek'lhri Return, and Vigilance) that must be completed with a Klingon character.
The Vigilance story arc is the fourth and final story arc to be completed as a Klingon character. It is made of four Episodes (primary missions):
1. A House Pursued
2. House on Fire
3. Alpha
4. Temporal Ambassador
After completing the fourth mission, this Achievement will unlock and you will have completed the Klingon-only Achievements.