To earn the "ESCAPE THE MANOR" trophy in Detroit: Become Human, you must reach the end of Kara's chapter "ZLATKO" alive. Note that Kara can be killed in this chapter, if she dies you will not only void this trophy but will also not be able to earn any other trophies involving Kara, including the trophy for getting all three characters to a certain point:
First off you will need to follow Zlatko through his conversation and down into the basement. Once you are in his machine, let everything play out until everyone leaves the room. Look left and down and push the trolley. Then look up and left and grab the wire. Finally kick your way out of the machine. Do this as quickly as possible so you don't lose any of your memory.
On the way back through the basement,
make sure to free the androids in the cell. Head upstairs and up the second flight. Head to where the android Luther stands still and enter the door next to him - there is an android polar bear in the corner that you should free. Head all the way to the last room on the upstairs corridor to get Alice.
Now there are a number of ways this can play out - you can hide, you can set the place on fire. I went into the room next to Alice's and hid under the table but fumbled it, so Luther spotted me immediately and kick-started the chase sequence. I'm happy to report that you can still survive if this happens, but I'm pretty certain it's crucial to have freed the polar bear and the androids downstairs. Just pay close attention to the quick-time events, almost always either
or
but sometimes mashing, sometimes hitting once within a limited time. I chose to rush at Zlatko when the choice was to evade or run right at him. I also chose the back door when prompted at the end of the chase sequence as I believe you will die if you head out of the front.
A scene plays out in the back yard and provided you freed the android monsters, Kara Alice and Luther should make it out fine. You will earn the trophy as soon as you reach the flowchart.