If you really want to finish this achievement as fast as possible, make sure to prioritize the 12–15-minute mission types called "Blitz: Search and Destroy" and "Eradicate". Play on the easier difficulties as it will be faster to complete each mission.
Don't worry about completing the sub-objectives and nests/factories as they are not necessary to "complete the mission". However, to be honest, I find just playing the game normally and focusing on the other achievements will bump this number up to where it needs to be.