Since yesterday, my Macbook Pro early 2013 running macOS High Sierra 10.13.1 beta has been randomly shutting down. After shutting down, it would take several tries for it to boot up and login, but then it displays this error message every time I login (see picture attached). I already tried resetting both PRAM and SMC, but the problem still occurs. Booting into safe mode wouldn't work when I pressed shift after the boot chime sound came (safe mode worked before this problem). Is there a way to fix this?
If a safe mode boot fails, you've got a damaged system.
Boot to recovery, internet recovery or external bootable media and reinstall the OS on top of all your existing apps and data. This preserves all data that's there.
If you suspect storage drive problems, you might check your last backup against another Mac to be sure it's up to date and restorable and possibly seek data recovery if you can't afford to lose the data before reinstalling the macOS.
I wouldn't do data recovery unless you have no backups and $300 or so for a professional service would be money well spent to safeguard your data. Most people recover from this with no data loss in about an hour or two after the reinstall starts, but I don't want you to not have the chance to back up before using the drive more if you suspect problems with the hardware and not just a third party extension causing lots of crashes.