By finishing the game under 4 hours, I unlocked
a circular saw and x-ray glasses
My next run was for "less than 3 medkits used" and "storage used less than 3 times" achievements (both successful), but this achievements didn't unlocked anything. Still, I know, that
Running Shoes and Essence of Defense Scroll
can be unlocked somehow. I still didn't complete all the coins, all files, and all Mr. Everywhere's achievements, but I'm not sure which of them may unlock things.
Best Answer
TL:DR These items may be earned by:
For your particular scenario (since you beat the game by only opening storage 3 times/under 4 hours already, and did not get all the Mr. Everywhere's), I would destroy all the Mr. Everywhere's. A guide can be found here if you wish to use one.
It appears that the Running Shoes may be unlocked by beating the game under a certain amount of time. Basically, as fast as you can muster.
This site said that on Easy-Mode and on their second play through, they beat it in under 4 hours and got the shoes:
However, the last link also states that the shoes can be earned by breaking all the bobble heads as well. This is making players suspect that the rewards at the end can be random. Another site claims that the shoes are earned by opening the item crate only 3 times and finishing the game, and that the circular saw it earned by beating the game in under four hours:
There is a Reddit Thread regarding the unlocks, and for the running shoes, they state that breaking all the bobble heads gets you them:
The same thread also says that by destroying all the bobble heads, they got the Essence of Defense Scroll:
Another site claims the same thing for the scroll:
To summarize, it appears that people are up in the air on how to specifically unlock this. Personally, I would destroy all 20 of the bobble heads and see if you unlock both since you have already done the other things the have been suggested across various websites. That way, you get two birds with one stone.