There is a glitch for this. You can start on Stage 4 (Factory) and complete the game from here to unlock this trophy. For that you should save as many workers and cats as you can. Time and health are very important for this run. I did it without purchasing anything from the store. That allowed me to also unlock
I have read that this glitch may not work if you have purchased a certain stat upgrade (unsure which one), so I did it without any upgrades.
I have also finished this on the PS4 from the beginning of the game. If you want to do it from the start then below is the guide for a proper run:
You should make a dedicated run for just this trophy. I tried many times whilst going for the harder save everyone trophies. When someone was downed, I would switch to speed running. The trouble is you waste too much time doing missions etc to make it worth while.
I had thought speed boots would be the best item for this one, but when I got the trophy I found that the Super Hose was the best. I got that at the first store and it allowed me to power through most rooms. I got the speed boots around the 4th shop which did speed me up.
The important part is to not go out of your way to save people. I tended to grab them when passing and if they died then no big deal. If they survived then I got an extra minute. I also bought the clock at the store if it was there. I saved almost all workers in the Office and Executive levels. This set me up with a large amount of time. I then save a few more in the labs and then stopped even bothering to get them.
The trick is to note the time when you start, and when you have enough remaining time to get to the end before the hour is out you can stop saving anyone.
I finished within 45 minutes on my first time trying to get this without doing anything else.