To earn the "MISSION ACCOMPLISHED" trophy in Detroit: Become Human, you need to complete the first chapter and save the girl at the end of it.
If you want to get this trophy as soon as possible, you can rush straight through the scene and play out the finale by walking straight out of the apartment's back windows and approaching the suspect. However your options in interacting with your target will be very limited as you will not have gathered much intel. How this then plays out can potentially have a knock-on effect on later events in the story and, in turn, other trophies tied to certain outcomes later in the game.
If you are going to rush through the game, you might as well make sure that Connor dies in the final sequence of the chapter to work towards:
To do this, head straight out of the back door and walk towards the subject without stopping. Pick options that suggest the target is defective. Wave the helicopter away when prompted and tell him that there are snipers on every roof. By this point you should get an option to Sacrifice Self. By doing so, you clock up one instance of Connor dying for the above trophy and unlock this trophy, as well as one for simply finishing the chapter: