This is a mandatory story achievement
~Spoilers for the last mission of the game~
After defeating Robo-Prez you then have to fight Silhouette as the final-final boss fight. This is a very difficult and long boss fight but with alot of patience can be done in 1 or 2 tries. I recommend looking up a boss guide if you're having difficulty with defeating her. Once you have defeated Silhouette the achievement should pop and this is the last story related achievement