Ok. Here's my tips on doing it in under 60 seconds. It's not as hard as it seems.
Start Sherry's segment. Instantly do a 180, grab the stuffed animal and inspect it to get the block. Run to the puzzle and put in the block.
Now since the puzzle is random you will need a piece of paper to write down the three starting blocks with each 4 showing symbol halfs (star, square, circle, triangle.)
When we load our autosave, we will be in the room and need to re-grab the block from the stuffed animal but the three blocks in the puzzle will not change positions.
Refer to this image for the solution:
Figure out how to solve your puzzle and take your time. We will re-load the autosave for our attempt at under 60 seconds in the room.
When solving the puzzle write down first how many rotations each block needs to fit into the solution. Do not worry about the last block (the block you place) it's rotation will be random each time you put it into the puzzle, so rotate it last.
Once you know how many rotations each block will need (one down, one up, or two up/down are all you need) then draw an arrow for each block that needs to be moved to let you know which position it needs to be in.
Once you know how to solve your puzzle, reload your save and get ready to get the block out, put it in the puzzle, rotate then move the blocks, then rotate your last block into the right spot. Grab the scissors from the puzzle and use them on the taped door and crotch out the exit. The achievement should pop right after. If not, reload your autosave and try again.
Make sure you know how to solve your puzzle and it should only take a couple moves. Remember that your block will be randomly rotated each time you put it in, so only it's position (block 1, 2, 3, 4) in the solution is important to remember.