Here is my 100% Achievement guide for The Great Perhaps.
A little bit through the game, you end up in a hospital/Mental ward.
We need to get the key from the guard on the first floor.
Go to 2nd floor and into the past you see a patient drawing on the wall. Here a cutscene will happen.
Immediately go into the future as to avoid being injected by the member of staff.
There is a gurney and blood splatter on the wall in the future, so grab the sponge and throw it sort of inbetween to get the big insects to come down.
Go to the 3rd floor, staying in the future and there is some huge ass flower to interact with. Doing so gives off a big pink stink where you can pick up a flower.
Into the past and the old guy talks to you wanting to go to the 4th floor, so push him to the right, avoiding guards as you go, hit the elvator button and take him all the way to the left.
Once that is done, head up to the 5th floor, in the middle of this area is a desk, interact with ti to put the flower in and the nurse thinks its the guard downstairs and voila, job done!
Go to 14:25 to see where and how to do this.
Hope this helps!