System won't boot after attempting 10.13.4 update
I had a similar problem with the 10.13.4 update. It failed to install and booted into Recovery Mode where the Console showed a file not found error in the logs and a menu to shutdown or restart. If restarted the system would again try to install the update and then fail the same way, resulting in a loop. Here is how I managed to fix it.

First I booted into Safe Mode (hold shift while booting) and started the update again from the Mac App Store. But this didn't succeed and the same problem appeared. I then booted again into Safe Mode, but this time deleted the folders which contained the update files which caused macOS to attempt to install the update every startup. These are the two folders I deleted

/macOS Install Data
/Library/Updates


This requires admin privileges. The easiest way is via the Terminal command sudo rm -rf /path/to/folder (Warning: Be sure that the path is right, otherwise you might delete your files. In any case make a backup of your drive first!). And even then it will tell you it can't delete all files in those folders because some are system protected but this is enough to solve the problem.

After deleting these folders I was able to boot up normally again although the system showed it was still on 10.13.3. I restarted the update in MAS again which then installed properly.