Have you tried it?
While booting, on the GRUB menu, press E.
You’ll see a bunch of code that looks like a shell script. Using the up and down arrow keys, find the line that starts with
linux /boot/vmlinuz-linux ...
go to the end of that line (press End), if the line is very long, your cursor may end up on the next line. Then type Space 3 (just add that, " 3" to the end of the line that starts with ‘linux’, nothing more). For example, in my case (in your case it will be different), I would have something like
linux /boot/vmlinuz-linux root=UUID=500a40b3-c412-4944-8f1d-9d8aee8a0a4b rw amd_iommu=on iommu=pt loglevel=3 nowatchdog
and I would change it to
linux /boot/vmlinuz-linux root=UUID=500a40b3-c412-4944-8f1d-9d8aee8a0a4b rw amd_iommu=on iommu=pt loglevel=3 nowatchdog 3
Then press Ctrl+X, and wait a minute or two, you should boot to the TTY1, where you’ll be prompted to enter your username and password (while entering the password, there is no echo, so no characters like ****, just type in the password blindly and press Enter).
Then, while in the terminal, type:
sudo pacman -Syu
And when it updates:
reboot
If you cannot do that, where does it fail? What do you see on your screen?
If you cannot even get to a TTY, then you’ll need to boot from a live image and chroot to your install, I can guide you through that process, but first make sure you absolutely cannot get to a TTY without the live ISO. From the error message you’re describing, your issue seems to be with the Light Display Manager (not monitor, but close enough). That comes fairly late in the boot process, so you should be able to access the TTY.
Obviously it probably has to do with his nvidia card updating. I wonder if he’s running just the nvidia? I run the nvidia-dkms as it seems to be way less problematic for nvidia drivers when updating.