1. Clean up any base, it doesnt matter if you take damage or not.

2. When the cutscene appears (the cutscene where all enemies are webbed up and you call Yuri), exit the game. Close it completely.

3. Start the game again and continue.

4. The game will show that you finished the base (no cutscene) and you will get your achievement.

Basically the game saves after completing the base but the damage is recorded after the cutscene, so when you close and open the game, the save continues from where it left but the damage record is gone, and your achievement pops up.