To get this, as the description says, you don't have to shoot or use flares during the boss fight against Mother and survive.
Here is a video of me getting the Trophy:
To achieve this, you have to move slowly and slightly backwards to dodge its attacks. You don't want to move fast because if you do so you will be cornered and you will die.
After dodging 2 or 3 attacks Mother will shriek and that's when you have the opportunity to quickly move forward and walk through it to get more room to maneuver.
After 2 minutes or so Mother will knock down the barrier on the right side and it will ran away.
Finally, go to sleep to get the Trophy.
